复杂动态网络的自适应同步控制研究
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摘要
复杂性与复杂系统是21世纪的重点研究课题之一.复杂网络是描述和理解复杂系统的重要工具和方法,它将复杂系统概括为由相互作用的多个个体（节点）组成的网络系统,广泛应用于不同的科学领域,如社会学、生物科学、计算机科学、物理学、工程学等,己成为复杂性科学领域中重要的研究课题.同步普遍存在于各类复杂网络系统中,是复杂网络上典型的集体行为,也是复杂网络最重要的动力学特性之一.复杂动态网络的同步控制是复杂网络研究和应用的关键环节,它以非线性动力学的研究为有效的理论基础和工具,并在保密通信、网络拥塞控制、调和振子生成、多智能体一致等领域有巨大的应用潜力.复杂动态网络的同步控制方法主要分两类:一类是通过改变网络本身的属性来提高网络的同步能力,如改变网络的拓扑结构、耦合强度等;另一类则是以控制理论研究为代表的控制方法,主要包括变量反馈控制、自适应控制、脉冲控制、牵制控制、滑模控制、驱动-响应同步等.
本文研究了复杂动态网络的同步控制问题,主要针对几类网络模型进行了研究,如时变复杂网络、具有耦合时滞的复杂网络、带有随机扰动的非线性耦合复杂动态网络、系统参数未知的时滞复杂网络及分数阶复杂动态网络等.以Lyapunov稳定性理论、随机微分方程理论、矩阵论、控制论为基础，主要使用自适应控制方法研究了这些复杂动力网络的同步控制问题,得到网络实现完全同步、投影同步及随机同步的一些准则,数值仿真验证了所得理论结果的有效性.全文分七章,第一章简要介绍了复杂网络及其同步控制的研究背景与进展,第二章到第六章为文章的正文,详细介绍了本文的工作.第七章指出论文的不足以及今后的工作展望.全文的主要研究工作概括如下:
1.基于Lyapunov稳定性理论和自适应控制及学习控制的方法,我们研究了时变耦合强度的复杂动态网络系统,通过设计适当的自适应学习控制器实现了网络的全局同步和平均同步.数值仿真表明了所给出的理论结果的正确性.
2.研究了时变复杂动态网络的投影同步问题,其中网络节点不要求是部分线性的,并且尺度因子可以是彼此不同的.基于Lyapunov稳定性理论,设计了适当的非线性自适应控制器得到实现投影同步的准则.最后研究了中立型时变耦合复杂动态网络,运用自适应策略达到同步.理论证明和数值仿真验证了所提方法的有效性.
3.研究了具有时变耦合时滞复杂动态网络的同步控制问题.所研究模型的耦合强度和耦合时滞均为时变的,运用自适应控制方法和反馈控制的思想,设计合适的控制器,实现了同时具有时滞与非时滞耦合的复杂动态网络的同步.通过构造Lyapunov-Krasovskii泛函给出理论证明,仿真实例进一步说明所得理论结果的正确性.
4.利用自适应控制方法,研究了时变复杂动态网络的非脆弱同步问题.考虑网络同步轨迹、拓扑信息等时变不确定因素,我们假设网络的耦合配置矩阵有界,内部耦合矩阵扰动范数意义有界,利用Lyapunov稳定性分析方法,得到实现时变复杂动态网络非脆弱同步的线性矩阵不等式(LMIs)条件.数值模拟的结果与理论分析一致.
5.研究了带有随机扰动的时变耦合复杂动态网络的同步控制问题.本章分别考虑了相同节点和不同节点的复杂动态网络在外部扰动下,利用随机微分方程理论及反馈控制方法得出了一些新的同步准则.理论分析和数值仿真均证明了所提同步方法的正确性
6.讨论了分数阶复杂动态网络系统的同步问题.基于分数阶系统稳定性理论,通过设计分数阶自适应控制器，实现了具有同节点的分数阶动态网络系统的同步，并得到了实现同步的充分条件
Complexity and complex systems are the important topics in the21st century. Complexnetworks are presently significant tools and methods to describe and understand the complexsystem, which highly summarize the complex system as the networks consisting of manyinteracting individuals or nodes. Complex networks have been used widely in different sci-entific fields, such as sociology, biological sciences computer sciences, physics, engineeringand so on, which have become a brilliant research topic of complexity science field. Syn-chronization is widespread in the various kinds of complicated network systems, and whichis a typical collective behavior in complex networks and one of the most important dynam-ic characteristics of complex networks as well. The research on the nonlinear dynamics areused as theoretical basis and tools for studying synchronization of complex networks. Syn-chronization control of complex dynamical networks is a key link of research and applicationof complex networks, and has great potential applications in secure communication, networkcongestion control, the generation of harmonic oscillator, multi-agent consensus, and so forth.Synchronization control method of complex dynamical networks is mainly divided into twokinds: one is to improve the network synchronization capability by changing the properties ofthe network itself, such as topology structure, coupling strength etc; another is to use controlmethod which is a representative of control theory, mainly including variable feedback con-trol method, adaptive control method, impulse control method, pinning control method, slidecontrol method, drive-response synchronization method.
This paper studies the synchronization control of complex dynamical networks. Somenetwork models are mainly studied, such as time-varying complex networks, dynamic net-works with time-varying delayed, nonlinearly coupled complex networks with stochastic per-turbations, dynamic networks with nonlinear derivative coupled, delayed complex networkswith uncertain system parameters and the fractional-order complex chaotic dynamical net-works etc. Based on Lyapunov stability theory, stochastic differential equation theory, matrixtheory, control theory, we use adaptive control methods to study the synchronization controlproblems of these complex dynamics networks, and obtain some criteria to realize complete-ly synchronization, projection synchronization. Numerical simulations are given to illustratethe effectiveness of the results. This paper is composed of seven chapters. In chapter1, weintroduced the background briefly and study progress of complex networks and synchroniza-tion control. Main results and ideas were given from Chapter2to Chapter6. Some existingproblems as well as the future research were pointed out in Chapter7. The main contributionsof this dissertation are summarized as follows:
1. Based on the Lyapunov stability theory, the adaptive control and the learning con- trol method, the complex dynamic network system with time-varying coupling strength isinvestigated. The appropriate adaptive learning controller is designed to achieve the globalsynchronization and average synchronization of the network proposed. Numerical simulationresults are performed to verify the validity of the presented method.
2. Projective synchronization in a time-varying dynamical network is considered, wherethe nodes are not necessarily partially linear and the scale factors may be different from eachother. Based on stability theorem, appropriate nonlinear adaptive controller are designed, wederive synchronization criteria for the projective synchronization. Finally, the neutral-typetime-varying coupling complex dynamic networks is studied, We use adaptive strategies toachieve synchronization of networks. Corresponding theoretical proofs and numerical simu-lations demonstrate the validity of the presented schemes.
3. The problem of the time-varying coupling time-varying delayed complex dynamicnetwork synchronization control is investigated. The coupling strength and coupling delayof the studied model are time-varying. Using adaptive control method and feedback control,we design some suitable controllers, the synchronization of complex dynamic network withdelayed and non-delayed coupling is realized. Theoretical proof is given by structured aLyapunov-Krasovskii functional. The simulation examples further illustrate the theoreticalresults is effective.
4. Using the adaptive control method, the non-fragile synchronization problem of time-varying complex dynamic network is investigated. Considering the network time-varyinguncertain factors such as synchronous track, topological information, we assume that the cou-pling configured matrix of network is bounded, the disturbance of internal coupling matrix isbounded in norm, using the Lyapunov stability method, the linear matrix inequality (LMIs)condition to achieve non-fragile synchronization of time-varying complex dynamic networkis obtained. The results of the numerical simulations are compatible with the theoretical anal-ysis.
5. We study synchronization control of time-varying coupled complex dynamical net-works with random disturbance. In this chapter, we consider the identical nodes and hetero-geneous nodes complex dynamic network with external perturbations, respectively. Some newsynchronization criteria are obtained by stochastic differential equation theory and feedbackcontrol method. Theoretical analysis and numerical simulations have verified the effectivenessof the proposed scheme.
6. Synchronization of the fractional-order complex dynamical networks is considered.Based on the stability theory of fractional-order systems, the fractional-order adaptive con-trollers are designed to realize synchronization of the fractional-order dynamical networkswith identical nodes, and a sufficient synchronization criteria is obtained.
本文研究了复杂动态网络的同步控制问题,主要针对几类网络模型进行了研究,如时变复杂网络、具有耦合时滞的复杂网络、带有随机扰动的非线性耦合复杂动态网络、系统参数未知的时滞复杂网络及分数阶复杂动态网络等.以Lyapunov稳定性理论、随机微分方程理论、矩阵论、控制论为基础，主要使用自适应控制方法研究了这些复杂动力网络的同步控制问题,得到网络实现完全同步、投影同步及随机同步的一些准则,数值仿真验证了所得理论结果的有效性.全文分七章,第一章简要介绍了复杂网络及其同步控制的研究背景与进展,第二章到第六章为文章的正文,详细介绍了本文的工作.第七章指出论文的不足以及今后的工作展望.全文的主要研究工作概括如下:
1.基于Lyapunov稳定性理论和自适应控制及学习控制的方法,我们研究了时变耦合强度的复杂动态网络系统,通过设计适当的自适应学习控制器实现了网络的全局同步和平均同步.数值仿真表明了所给出的理论结果的正确性.
2.研究了时变复杂动态网络的投影同步问题,其中网络节点不要求是部分线性的,并且尺度因子可以是彼此不同的.基于Lyapunov稳定性理论,设计了适当的非线性自适应控制器得到实现投影同步的准则.最后研究了中立型时变耦合复杂动态网络,运用自适应策略达到同步.理论证明和数值仿真验证了所提方法的有效性.
3.研究了具有时变耦合时滞复杂动态网络的同步控制问题.所研究模型的耦合强度和耦合时滞均为时变的,运用自适应控制方法和反馈控制的思想,设计合适的控制器,实现了同时具有时滞与非时滞耦合的复杂动态网络的同步.通过构造Lyapunov-Krasovskii泛函给出理论证明,仿真实例进一步说明所得理论结果的正确性.
4.利用自适应控制方法,研究了时变复杂动态网络的非脆弱同步问题.考虑网络同步轨迹、拓扑信息等时变不确定因素,我们假设网络的耦合配置矩阵有界,内部耦合矩阵扰动范数意义有界,利用Lyapunov稳定性分析方法,得到实现时变复杂动态网络非脆弱同步的线性矩阵不等式(LMIs)条件.数值模拟的结果与理论分析一致.
5.研究了带有随机扰动的时变耦合复杂动态网络的同步控制问题.本章分别考虑了相同节点和不同节点的复杂动态网络在外部扰动下,利用随机微分方程理论及反馈控制方法得出了一些新的同步准则.理论分析和数值仿真均证明了所提同步方法的正确性
6.讨论了分数阶复杂动态网络系统的同步问题.基于分数阶系统稳定性理论,通过设计分数阶自适应控制器，实现了具有同节点的分数阶动态网络系统的同步，并得到了实现同步的充分条件
Complexity and complex systems are the important topics in the21st century. Complexnetworks are presently significant tools and methods to describe and understand the complexsystem, which highly summarize the complex system as the networks consisting of manyinteracting individuals or nodes. Complex networks have been used widely in different sci-entific fields, such as sociology, biological sciences computer sciences, physics, engineeringand so on, which have become a brilliant research topic of complexity science field. Syn-chronization is widespread in the various kinds of complicated network systems, and whichis a typical collective behavior in complex networks and one of the most important dynam-ic characteristics of complex networks as well. The research on the nonlinear dynamics areused as theoretical basis and tools for studying synchronization of complex networks. Syn-chronization control of complex dynamical networks is a key link of research and applicationof complex networks, and has great potential applications in secure communication, networkcongestion control, the generation of harmonic oscillator, multi-agent consensus, and so forth.Synchronization control method of complex dynamical networks is mainly divided into twokinds: one is to improve the network synchronization capability by changing the properties ofthe network itself, such as topology structure, coupling strength etc; another is to use controlmethod which is a representative of control theory, mainly including variable feedback con-trol method, adaptive control method, impulse control method, pinning control method, slidecontrol method, drive-response synchronization method.
This paper studies the synchronization control of complex dynamical networks. Somenetwork models are mainly studied, such as time-varying complex networks, dynamic net-works with time-varying delayed, nonlinearly coupled complex networks with stochastic per-turbations, dynamic networks with nonlinear derivative coupled, delayed complex networkswith uncertain system parameters and the fractional-order complex chaotic dynamical net-works etc. Based on Lyapunov stability theory, stochastic differential equation theory, matrixtheory, control theory, we use adaptive control methods to study the synchronization controlproblems of these complex dynamics networks, and obtain some criteria to realize complete-ly synchronization, projection synchronization. Numerical simulations are given to illustratethe effectiveness of the results. This paper is composed of seven chapters. In chapter1, weintroduced the background briefly and study progress of complex networks and synchroniza-tion control. Main results and ideas were given from Chapter2to Chapter6. Some existingproblems as well as the future research were pointed out in Chapter7. The main contributionsof this dissertation are summarized as follows:
1. Based on the Lyapunov stability theory, the adaptive control and the learning con- trol method, the complex dynamic network system with time-varying coupling strength isinvestigated. The appropriate adaptive learning controller is designed to achieve the globalsynchronization and average synchronization of the network proposed. Numerical simulationresults are performed to verify the validity of the presented method.
2. Projective synchronization in a time-varying dynamical network is considered, wherethe nodes are not necessarily partially linear and the scale factors may be different from eachother. Based on stability theorem, appropriate nonlinear adaptive controller are designed, wederive synchronization criteria for the projective synchronization. Finally, the neutral-typetime-varying coupling complex dynamic networks is studied, We use adaptive strategies toachieve synchronization of networks. Corresponding theoretical proofs and numerical simu-lations demonstrate the validity of the presented schemes.
3. The problem of the time-varying coupling time-varying delayed complex dynamicnetwork synchronization control is investigated. The coupling strength and coupling delayof the studied model are time-varying. Using adaptive control method and feedback control,we design some suitable controllers, the synchronization of complex dynamic network withdelayed and non-delayed coupling is realized. Theoretical proof is given by structured aLyapunov-Krasovskii functional. The simulation examples further illustrate the theoreticalresults is effective.
4. Using the adaptive control method, the non-fragile synchronization problem of time-varying complex dynamic network is investigated. Considering the network time-varyinguncertain factors such as synchronous track, topological information, we assume that the cou-pling configured matrix of network is bounded, the disturbance of internal coupling matrix isbounded in norm, using the Lyapunov stability method, the linear matrix inequality (LMIs)condition to achieve non-fragile synchronization of time-varying complex dynamic networkis obtained. The results of the numerical simulations are compatible with the theoretical anal-ysis.
5. We study synchronization control of time-varying coupled complex dynamical net-works with random disturbance. In this chapter, we consider the identical nodes and hetero-geneous nodes complex dynamic network with external perturbations, respectively. Some newsynchronization criteria are obtained by stochastic differential equation theory and feedbackcontrol method. Theoretical analysis and numerical simulations have verified the effectivenessof the proposed scheme.
6. Synchronization of the fractional-order complex dynamical networks is considered.Based on the stability theory of fractional-order systems, the fractional-order adaptive con-trollers are designed to realize synchronization of the fractional-order dynamical networkswith identical nodes, and a sufficient synchronization criteria is obtained.
引文
[1]郝柏林.分岔、混沌、奇怪吸引子、湍流及其他—-关于确定论系统中的内在随机性.物理学进展,3(3):329–416,1983.
[2] Watts D.J. and Strogatz S.H. Collective dynamics of”small-world” networks. Nature,393:440–442,1998.
[3] Baraba′si A.L. and Albert R. Emergence of scaling in random networks. Science,286(10):509–512,1999.
[4] Jeong H., Tombor B., Albert R., Oltvai Z. N., and Baraba′si A.L. The large-scale organization ofmetabolic networks. Nature,407:651–654,2000.
[5] Ebel H., Mielsch L., and Bornholdt S. Scale-free topology of e-mail networks. Physical Review E,66(3):035103,2002.
[6] Li W. and Cai X. Statistical analysis of airport network of china. Physical Review E,69(4):046106,2004.
[7] Boccaletti S., Latora V., Moreno Y., Chavez M., and Hwang D.U. Complex networks: structure anddynamics. Physics Reports,424(4-5):175–308,2006.
[8] Bond J. and Murty U.S.R. Groph Theory with Applications. London and Basingstoke, MacMillanPress LTD,1976.
[9] Xu J. M. Topological Structure and Analysis of Interconnection Network. London, Kluwer AeademicPublishers,2001.
[10] Erdo¨s P. and Re′nyi A. On random graphs. Published in Math Debrecen,1959.
[11] Erdo¨s P. and Re′nyi A. On the evolution of random graphs. Publications of the Mathematical Instituteof the Hungarian Academy of Science,5(1):17–61,1960.
[12] Erdo¨s P. and Re′nyi A. On the strength of connectedness of a random graph. Acta MathematicaScientia Hungary,12:261–267,1961.
[13] Bolloba′s B. Random Graphs. New York, Academic Press,2001.
[14] Strogatz S. H. Exploring complex networks. Nature,410:268–276,2001.
[15] Albert R. and Baraba′si A. L. Statistical mechanics of complex networks. Reviews of Modern Physics,74(1):47–97,2002.
[16] Wang W. X., Wang B.H., Hu B., Yan G., and Ou Q. General dynamics of topology and traffic onweighted technological networks. Physical Review Letters,95(18):188702,2005.
[17]方锦清，李永.网络科学中统一混合理论模型的若干研究进展.力学进展,38(6):663–678,2008.
[18]刘宏鲲，张效莉，曹莨，汪秉宏，周涛.中国城市航空网络航线连接机制分析.中国科学G辑,39(7):935–942,2009.
[19] Wu C.W. Synchronization in complex networks of nonlinear dynamical systems. Singapore: WorldScientific,2007.
[20] Diaz-Guilera A. Kurths J. Moreno Y. Zhou C. Arenas, A. Synchronization in complex networks.Physics Reports,469(3):93–153,2008.
[21]赵明，周涛，陈关荣，汪秉宏.复杂网络上动力系统同步的研究进展―如何提高网络的同步能力.物理学进展,28(1):22–34,2008.
[22] Sun Y.G. and Wang L. Consensus problems in networks of agents with double-integrator dynamicsand time-varying delays. International Journal of Control,82(10):1937–1945,2009.
[23] Vespignani A. Complex networks: The fragility of interdependency. Nature,464:984–985,2010.
[24] Buldyrev S.V., Parshani R., Paul G., Stanley H.E., and Havlin S. Catastrophic cascade of failures ininterdependent networks. Nature,464:1025–1028,2010.
[25] Li X., Wang X. F., and Chen G. Pinning a complex dynamical network to its equilibrium. IEEETrans. on Circuits and Systems I,51(10):2074–2087,2004.
[26]汪小帆，李翔，陈关荣.复杂网络理论及其应用.北京：清华大学出版社,2006.
[27] Newman M E J. and Watts D.J. Renormalization group analysis of the small-world network model.Physics Letters A,263(4-6):341–346,1999.
[28]赵明.复杂网络上动力系统同步现象的研究. PhD thesis,合肥:中国科学技术大学,2007.
[29] Pecora L.M. and Carroll T.L. Master stability functions for synchronized coupled systems. PhysicalReview Letters,80(10):2109–2112,1998.
[30] Wang X.F. Complex networks: topology, dynamics and synchronization. International Journal ofBifurcation&Chaos,12(5):885–916,2002.
[31] Wang X.F. and Chen G. Synchronization in small-world dynamical networks. International Journalof Bifurcation&Chaos,12(1):187–192,2002.
[32] Barahona M. and Pecora L.M. Synchronization in small-world systems. Physical Review Letters,89(5):054101,2002.
[33] Hu G., Yang J., and Liu W. Instability and controllability of linearly coupled oscillators: Eigenvalueanalysis. Physical Review E,58(4):4400–4453,1998.
[34] Zhao J., Hall D. J., and Liu T. Synchronization of dynamical networks with nonidentical nodes:Criteria and control. IEEE Transactions on Circuits and Systems I,58(3):584–594,2011.
[35] Chen Y., Rangarajan G., and M. Ding. General stability analysis of synchronized dynamics incoupled systems. Physical Review E,67(4):026209,2003.
[36] Belykh V., Belykh I., and Hasler M. Connection graph stability method for synchronized coupledchaotic systems. Physica D,195(1-2):159–187,2004.
[37] Lu W. and Chen T. New approach to synchronization analysis of linearly coupled ordinary diffrentialsystems. Physica D,213(2):214–230,2006.
[38] Chen T. and Zhu Z.M. Exponential synehronization of nonlinear coupled dynamical networks.International Journal of Bifurcation&Chaos,17(3):999–1005,2007.
[39] Leyva I., Sendina-Nadal I., Almendral J. A., and Sanjnan M. A. F．. Sparse repulsive couplingenhances synchronization in complex networks. Physical Review E,74:056112,2006.
[40] Stilwell D. J., Bollt E., and Roberson D. Sufficient conditions for fast switching synchronizationin time-varying network topologies. SIAM Journal on Applied Dynamical System,5(1):140–156,2006.
[41] Lu¨ J. and Chen G. A time-varying complex dynamical network model and its controlled synchro-nization criteria. IEEE Transactions on Automatic Control,50(6):841–846,2005.
[42] Lu¨ J., Yu X., and Chen G. Chaos synchronization of general dynamical networks. Physica A,334(1-2):281–302,2004.
[43] Boccaletti S., Hwang D. U., Chavez M., Amann A., Kurths J., and Pecora M. Synchronization indynamical networks：evolution along commutative graphs. Physical Review E,74:016102,2006.
[44] Ito J. and Kaneko K. Spontaneous structure formation in a network of chaotic units with variableconnection strengths. Physical Review Letters,88(2):028701,2001.
[45] Zanette D. H. and Mikhailov A. S. Dynamical systems with time-dependent coupling：clusteringand critical behavior. Physica D,194(3-4):203–218,2004.
[46] Porfiri M., Stilwell D. J., Bollt E. M., and Skufca J. D. Random talk: Random walk and synchroniz-ability in a moving neighborhood network. Physica D,224(1-2):102–113,2006.
[47] Jadbabaie A., Lin J., and Morse A. S. Coordination of groups of mobile autonomous agents usingnearest neighbor rules. IEEE Transactions on Automatic Control,48:988–1001,2003.
[48] Ogren P., Fiorelli E., and Leonard N. E. Cooperative control of mobile sensor networks：adaptivegradient climbing in a distributed environment. IEEE Transactions on Automatic Control,49:1292–1302,2004.
[49] Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Trans-actions on Automatic Control,50:169–182,2005.
[50] Xiao F. and Wang L. State consensus for multi-agent systems with switching topologies and time-varying delays. International Journal of Control,79:1277–1284,2006.
[51] Xie G. and Wang L. Consensus control for a class of networks of dynamic agents. InternationalJournal of Robust Nonlinear Control,17:941–959,2007.
[52] Hong Y., Hua J., and Gao L. Lyapunov-based approach to multi-agent systems with switching jointlyconnected interconnection. IEEE Transactions on Automatic Control,52:943–948,2007.
[53] Frasca M., Buscarino A., Rizzo A., Fortuna L., and Boccaletti S. Synchronization of moving chaoticagents. Physical Review Letters,100:044102,2008.
[54] Buscarino A., Fortuna L., and Frasca M. Dynamical network interactions in distributed control ofrobots. Chaos,16:015116,2006.
[55] Dan S., S rensen P. G., and Hynne F. Sustained oscillations in living cells. Nature,402:320–322,1999.
[56] Dan S., Hynne F., and Monte S. D. Synchronization of glycolitic oscillations in intact yeast cells.Faraday Discuss,120:261–276,2001.
[57] Lu¨ J.H. and Chen G. A time-varying complex dynamical network model and its controlled synchro-nization criteria. IEEE Transactions on Automatic Control,50(6):841–846,2005.
[58] Daniel J. S., Erik M. B., and Roberson D. G. Synchronization of time-varying networks under fastswitching. In Proceedings of the2006American Control Conference,2006.
[59] Belykh I. V., Hasler M., Laurent M., and Nijmeijer. Psynchronization and graph topology. Interna-tional Journal of Bifurcation and Chaos,15(11):3423–3433,2005.
[60] Belykh I., Belykh V., and Hasler M. Generalized connection graph method for synchronization inasymmetrical networks. Physica D,224(1-2):42–51,2006.
[61] Chen M. Y. Synchronization in time-varying networks：a matrix measure approach. PhysicalReview E,76:016104,2007.
[62] Zhang R., Hu M., and Xu Z. Synchronization in complex networks with adaptive coupling. Phys.Lett. A,368(8):276–280,2007.
[63] Li Z., Jiao L., and Lee J.J. Robust adaptive global synchronization of complex dynamical networksby adjusting time-varying coupling strength. Physica A,387(5-6):1369–1380,2008.
[64] Liu H., Chen J., Lu J., and Cao M. Generalized synchronization in complex dynamical networks viaadaptive couplings. Physica A,389(8):1759–1770,2010.
[65] Lu J. and Cao J. Adaptive synchronization of uncertain dynamical networks with delayed coupling.Nonlinear Dynamics,53(1-2):107–115,2008.
[66] Yeung M. K. S. and Strogatz S. H. Time delay in the kuramoto model of coupled oscillators. PhysicalReview Letters,82(3):648–651,1999.
[67] Heil T., Fischer I., and Elsasser W. Chaos synchronization and spontaneous symmetry-breaking insymmetrically delay-coupled semiconductor lasers. Physical Review Letters,86(5):795–798,2001.
[68] Strogatz S. H. Death by delay. Nature,394:316–317,1998.
[69] Reddy D. V. R., Sen A., and Johnston G. L. Time delay induced death in coupled limit cycleoscillators. Physical Review Letters,80(23):5109–5112,1998.
[70] Niebur E., Schuster H. G., and Kammen D. M. Collective frequencies and metstability in networksin limit-cycle oscillators with time delay. Physical Review Letters,67(20):2753–2756,1991.
[71] Li C. and Chen G. Sychronization in general complex dynamical networks with coupling delays.Physica A,343:263–278,2004.
[72] Gao H., Lam J., and Chen G. New criteria for synchronization stability of general complex dynam-ical networks with coupling delays. Phys. Lett. A,360(2):263–273,2006.
[73] Wang Q., Chen G., Lu Q., and Hao F. Novel criteria of synchronization stability in complex networkswith coupling delays. Physica A,378(2):527–536,2007.
[74] Li C. P., Sun W. G., and Kurths J. Synchronization of complex dynamical networks with time delays.Physica A,361(1):24–34,2006.
[75] Li P., Yi Z., and Zhang L. Global synchronization of a class of delayed complex networks.Chaos，Solitons&Fractals,30(4):903–908,2006.
[76] Lu W., Chen T., and Chen G. Synchronization analysis of linearly coupled systems described bydiffrential equations with a coupling delay. Physica D,221(2):118–134,2006.
[77] Liu X. and Chen T. P. Exponential synchronization of nonlinear coupled dynamical networks with adelayed coupling. Physica A,381:82–92,2007.
[78] Liu B., Teo K. L., and Liu X. Global synchronization of dynamical networks with coupling timedelays. Physics Letters A,368(1-2):53–63,2007.
[79] Wang L., Dai H. P., and Sun Y. X. Synchronization criteria for a generalized complex delayeddynamical network model. Physica A,383(2):703–713,2007.
[80] Zhou J., Xiang L., and Liu Z. R. Synchronization in complex delayed dynamical networks withimpulsive effects. Physica A,384(2):684–692,2007.
[81] Zhou J., Xiang L., and Liu Z. R. Global synchronization in general complex delayed dynamicalnetworks and its applications. Physica A,385(2):729–742,2007.
[82] Yang M., Wang Y., and Wang K. Delay independent synchronization of complex network via hybridcontrol. In ACC’08, pages2266–2271,2008.
[83] Cai S., Zhou J., Xiang L., and Liu Z. Robust impulsive synchronization of complex delayed dynam-ical networks. Phys. Lett. A,372(30):4990–4995,2008.
[84] Chen G R，Zhou J，Liu Z R．. Global synchronization of coupled delayed neural networks andapplications to chaotic cnn model. International Journal of Bifurcation and Chaos,14(7):2229–2240,2004.
[85] Lu W. L. and Chen T. P. Synchronization of coupled connected neural networks with delays. IEEETransactions Circuits System-I,51(12):2491–2503,2004.
[86] Wang W. and Cao J. Synchronization in an array of linearly coupled networks with time-varyingdelay. Physica A,366(1):197–211,2006.
[87] Sun Y., Cao J., and Wang Z. Exponential synchronization of stochastic perturbed chaotic delayedneural networks. Neurocomputing,70(13-15):2477–2485,2007.
[88] Hua C., Wang Q., and Guan X. Global adaptive synchronization of complex networks with nonlineardelay coupling interconnections. Physics Letters A,368(3-4):281–288,2007.
[89] Li Z., Feng G., and Hill D. Controlling complex dynamical networks with coupling delays to adesired orbit. Phys. Lett. A,359(1):42–46,2006.
[90] Lu J. Q., Ho D. W. C., and Liu M. Globally exponential synchronization in an array of asymmetriccoupled neural networks. Physics Letters A,369(5-6):444–451,2007.
[91] Liu T., Dimirovski G. M., and Zhao J. Exponential synchronization of complex delayed dynamicalnetworks with general topology. Physica A,387(2-3):643–652,2008.
[92] Wu J. and Jiao L. Synchronization in dynamic networks with nonsymmetrical time-delay couplingbased on linear feedback controllers. Physica A,387(8-9):2111–2119,2008.
[93]罗群，吴薇，李丽香，杨义先，彭海朋.节点含时滞的不确定复杂网络的自适应同步研究.物理学报,57(3):1529–1534,2008.
[94] Yu W., Cao J., and Lu J. Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM Journal on Applied Dynamical Systems,7(1):108–133,2008.
[95] Dai Y., Cai Y., and Xu X. Synchronization criteria for complex dynamical networks with neutral-type coupling delay. Physica A,387(18):4673–4682,2008.
[96] He Y., Wu M., She J.H., and Liu G.P. Delay-dependent robust stability criteria for uncertain neutralsystems with mixed delays. Systems&Control Letters,51(1):57–65,2004.
[97] Yao J., Wang H.O., Guan Z.H., and Xu W. Passive stability and synchronization of complex spatio-temporal switching networks with time delays. Automatica,45(7):1721–1728,2009.
[98] Yue D. and Li H. Synchronization stability of continuous/discrete complex dynamical networks withinterval time-varying delays. Neurocomputing,73(4-6):809–819,2010.
[99] Wang X. and Chen G. Synchronization in small-world dynamical net-works. International Journalof Bifurcation and Chaos,12(1):187–192,2002.
[100] Wang X. and Chen G. Synchronization in scale-free dynamical net-works: robustness and fragility.IEEE Trans. on Circuits and Systems I,49(1):54–62,2002.
[101] Gu Z.M., Zhao M., Zhou T., Zhu C.P., and Wang B.H. Phase synchronization of non-abelian oscil-lators on small-world networks. Physics Letters A,362(2-3):115–119,2007.
[102] Fumito M. and Takashi O. Synchronization of coupled oscillators on small-world networks. PhysicaD,238(14):1180–1185,2009.
[103] Zou Y. and Chen G. Choosing effective controlled nodes for scale-free network synchronization.Physica A,388(14):2931–2940,2009.
[104] Sorrentino F., di Bernardo M., Huerta Cue′llar G., and Boccaletti S. Synchronization in weightedscale-free networks with degree-degree correlation. Physica D,224(1-2):123–129,2006.
[105] Duan Z., Chen G., and Huang L. Synchronization of weighted networks and complex synchronizedregions. Physics Letters A,372(21):3741–3751,2008.
[106] Wu X. and Lu H. Exponential synchronization in delayed and non-delayed coupling dynamicalnetworks. Computers and Mathematics with Applications,60(8):2476–2487,2010.
[107] Li C., Sun W., and Kurths J. Synchronization between two coupled complex networks. PhysicalReview E,76(4):046204,2007.
[108] Wu X. and Lu H. Cluster synchronization in the adaptive complex dynamical networks via a novelapproach. Physics Letters A,375(14):1559–1565,2011.
[109] Liu H., Lu J.A., Lu¨ J., and Hill D.J. Structure identification of uncertain general complex dynamicalnetworks with time delay. Automatica,45(8):1799–1807,2009.
[110] Tang Y., Wang Z., and Fang J. Pinning control of fractional-order weighted complex networks.Chaos,19(1):013112,2009.
[111] Tang Y. and Fang J. Synchronization of n-coupled fractional-order chaotic systems with ring con-nection. Commun. Nonlinear Sci. Numer. Simulat.,15(2):401–412,2010.
[112] Wang J. and Zhang Y. Network synchronization in a population of star-coupled fractional nonlinearoscillators. Phys. Lett. A,374(13-14):1464–1468,2010.
[113] Wu X. and Lu H. Outer synchronization of two different fractional-order complex dynamical net-works. Chinese Physics B.,19(7):070511,2010.
[114] Hu G. and Qu Z. L. Controlling spatiotemporal chaos in coupled map lattice systems. PhysicalReview Letters,72(1):68–71,1994.
[115] Wang X. and Chen G. Pinning control of scale-free dynamical networks. Phycica A,310(3-4):521–531.,2002.
[116] Fan Z. and Chen G. Pinging control of scale-flee complex networks. IEEE International Symposiumon Circuits and Systems，Kobe，Japan,1:284–287,2005.
[117] Liu Z., Chen Z., and Yuan Z. Pinning control of weighted general complex dynamical networks withtime delay. Physica A,375(1):345–354,2007.
[118] Chen T., Liu X., and Lu W. Pinning complex networks by a single controller. IEEE Trans. CircuitsSyst. I,54(6):1317–1326,2007.
[119] Feng J.W., Sun S.H., Xu C., Zhao Y., and Wang J.Y. The synchronization of general complexdynamical network via pinning control. Nonlinear Dynamics,67(2):1623–1633,2012.
[120] Porfiri M. and Bernardo M. D. Criteria for global pinning-controllability of complex networks.Automatics,44(12):3100–3106,2008.
[121] Zhou J., Lu J. A., and Lu¨ J. H. Pinning adaptive synchronization of a general complex dynamicalnetwork. Automatica,44(4):996–1003,2008.
[122] Guo W., Austin F. Chen S., and Sun W. Pinning synchronization of the complex networks withnon-delayed and delayed coupling. Physics Letters A,373(17):1565–1572,2009.
[123] Ma Q. and Lu J. Cluster synchronization for directed complex dynamical networks via pinningcontrol. Neurocomputing,101(4):354–360,2013.
[124] Su H.S., Rong Z.H., Chen M.Z.Q., Wang X.F., Chen G.R., and Wang H.W. Decentralized adaptivepinning control for cluster synchronization of complex dynamical networks. IEEE Transactions onCybernetics,43(1):394–399,2013.
[125] Xiong W., Ho D. W. C., and Huang C. Pinning synchronization of time-varying polytopic directedstochastic networks. Physics Letters A,374(3):439–447,2010.
[126]姚静，关治洪.拓扑切换网络的脉冲控制.复杂系统与复杂性科学,2(2):24–29,2005.
[127] Yao J., Guan Z. H., and Hill DV Wang H O. On passivity and impulsive control of complex dynam-ical networks with coupling delays. In Proceeding of the44m IEEE conference on Decision andcontrol．and the European Control Conference2005, pages1595–1600,2005.
[128] Guan Z. H. and Zhang H. Stabilization of complex network with hybrid impulsive and switchingcontrol. Chaos，Solitons&Fractals,37(5):1372–1382,2008.
[129] Liu B., Liu X. Z., Chen G., and Wang H. Y. Robust impulsive synchronization of uncertain dynam-ical networks. IEEE Transactions on Circuits&Systems I,52(2):1431–1441,2005.
[130] Ma Z J．Zhang G，Liu Z R. Synchronization of complex dynamical networks via impulsive con-trol. Chaos,17(4):043126,2007.
[131] Li P., Cao J., and Wang Z. Robust impulsive synchronization of coupled delayed neural networkswith uncertainties. Physica A,373(1):261–272,2007.
[132] Zhou J., Q.J. Wu, and Xiang L. Pinning complex delayed dynamical networks by a single impulsivecontroller. IEEE Transactions on Circuits and Systems I,58(12):2882–2893,2011.
[133] Yang Y. Q. and Cao J. D. Exponential lag synchronization of a class of chaotic delayed neuralnetworks with impulsive effects. Physica A,386(1):492–502,2007.
[134] Jiang H. B. Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical net-works by the generalised barbalat’s lemma. IET Control Theory&Applications,3(10):1330–1340,2009.
[135] Huang D. B. Simple adaptive-feedback controller for identical chaos synchronization. PhysicalReview E,71(3):037203,2005.
[136] Sun M., Zeng C. Y., and Tian L. X. Projective synchronization in drive-response dynamical networksof partially linear systems with time-varying coupling delay. Physics Letters A,372(46):6904–6908,2008.
[137] Wen S., Chen S., and Guo W. Adaptive global synchronization of a general complex dynamicalnetwork with non-delayed and delayed coupling. Phys. Lett. A,372(42):6340–6346,2008.
[138] Wang K., Teng Z. D., and Jiang H. J. Adaptive synchronization of neural networks with time-varyingdelay and distributed delay. Physica A,387()2-3:631–642,2008.
[139] Li Z. and Chen G. Robust adaptive synchronization of uncertain dynamical networks. Phys. Lett. A,324(2-3):166–178,2004.
[140] Zhou J., Lu J., and Lu¨ J. Adaptive synchronization of an uncertain complex dynamical network.IEEE Trans. on Automatic Control,51(4):652–656,2006.
[141] Chen M. Y. and Zhou D. H. Synchronization in uncertain complex networks. Chaos,16(1):013101,2006.
[142] Lu W. L. Adaptive dynamical networks via neighborhood information：synchronization and pin-ning control. Chaos,17(2):023122,2007.
[143] Li K., Small M., and Fu X. Generation of clusters in complex dynamical networks via pinningcontrol. Journal of Physics A：Mathematical and General,41:505101,2008.
[144] Wu X. Synchronization-based topology identification of weighted general complex dynamical net-works with time-varying coupling delay. Physica A,387(4):997–1008,2008.
[145] Zheng S., Bi Q., and Cai G. Adaptive projective synchronization in complex networks with time-varying copling delay. Physics Letters A,373(17):1553–1559,2009.
[146] Zhou J. and Lu J. A. Topology identification of weighted complex dynamical networks. Physica A,386(1):481–491,2007.
[147]张青，杨正全，陈增强.带有未知参数的复杂动态网络的自适应同步(英文).南开大学学报(自然科学版),43(4):7–14,2010.
[148] Xiao X. Y., Xu W., Li X. C., and Tang S. F. Adaptive complete synchronization of chaotic dynamicalnetwork with unknown and mismatched parameters. Chaos,17(3):033118,2007.
[149] Yu W. W. and Cao J. D. Adaptive synchronization and lag synchronization of uncertain dynamicalsystem with time delay based on parameter identification. Physica A,375(2):467–482,2007.
[150] Mahdavi N., Menhaj M.B., Kurths J., and Lu J. Fuzzy complex dynamical networks and its syn-chronization. IEEE Transactions on Cybernetics,43(2):648–659,2013.
[151]卢文联.动力系统与复杂网络：理论与应用. PhD thesis,上海：复旦大学,2005.
[152] Arenas A., Diaz-Guilera A., Kurths J., Moreno Y., and Zhou C. Synchronization in complex net-works. Physics Reports,469(3):93–153,2008.
[153] Pecora L.M. and Carroll T.L. Master stability functions for synchronized coupled systems. PhysicalReview Letters,80(10):2109–2112,1998.
[154] Du H., Shi P., and Lu¨ N. Function projective synchronization in complex dynamical networks withtime delay via hybrid feedback control. Nonlinear Analysis: Real World Applications,14(2):1182–1190,2013.
[155] Ma Z.J., Liu Z.R., and Zhang G. A new method to realize cluster synchronization in connectedchaotic networks. Chaos,16(2):023103,2006.
[156] Wu W., Zhou W., and Chen T. Cluster synchronization of linearly coupled complex networks underpinning control. IEEE Trans. on Circuits and Systems I,56(4):829–839,2009.
[157] Zhao J.C., Aziz-Alaoui M. A., and Bertelle C. Cluster synchronization analysis of complex dynam-ical networks by input-to-state stability. Nonlinear Dynamics,70(2):1107–1115,2012.
[158] Yu L., Tu L.L., and Liu H.F. Adaptive cluster synchronization for a complex dynamical networkwith delays and stochastic perturbation. The European Physical Journal B,86:130,2013.
[159] Kaneko K. Relevance of clustering to biological networks. Physica D,75:55–73,1994.
[160] Belykh I., Belykh V., Nevidin K., and Hasler M. Persistent clusters in lattices of coupled nonidenticalchaotic systems. Chaos,13(1):165–178,2003.
[161] Cao J. and Li L. Cluster synchronization in an array of hybrid coupled neural networks with delay.Neural Networks,22(4):335–342,2009.
[162] Newman M.E.J. The structure and function of complex networks. SIAM Review,45(2):167–256,2003.
[163] Wu C. Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuits Syst. II,52(5):282–286,2005.
[164] Li Z., Jiao L., and Lee J. Robust adaptive global synchronization of complex dynamical networksby adjusting time-varying coupling strength. Physica A,387(5-6):1369–1380,2008.
[165] Wang Y.H., Fan Y.Q., Wang Q.Y., and Zhang Y. Stabilization and synchronization of complex dy-namical networks with different dynamics of nodes via decentralized controllers. IEEE Transactionson Circuits and Systems I,59(8):1786–1795,2012.
[166] Guo W., Chen S., and Sun W. Topology identification of the complex networks with non-delayedand delayed coupling. Phys. Lett. A,373(41):3724–3729,2009.
[167] Xu Y., Zhou W., Fang J., Sun W., and Pan L. Topology identification and adaptive synchronizationof uncertain complex networks with non-derivative and derivative coupling. Journal of the FranklinInstitute,347(4):1566–1576,2010.
[168] Song Y., Yu X., Chen G., Xu J., and Tian Y. Time delayed repetitive learning control for chaoticsystems. Int. J. Bifur. Chaos,12(5):1057–1066,2002.
[169] Xu J. and Yan R. On repetitive learning control for periodic tracking tasks. IEEE Trans. Autom.Control,51(11):1842–1848,2006.
[170] Tao G. A simple alternative to the barbalat lemma. IEEE Transactions on Automatic Control,42(5):698–698,1997.
[171] Sun M. A barbalat-like lemma with its application to learning control. IEEE Transactions onAutomatic Control,54(9):2222–2225,2009.
[172] Guo X.，Li J. Projective synchronization of complex dynamical networks with time-varying cou-pling strength via hybrid feedback control. Chinese Physics Letters,28(12):120503,2011.
[173] Xu Y., Zhou W., Fang J., and Sun W. Adaptive synchronization of the complex dynamical networkwith non-derivative and derivative coupling. Phys. Lett. A,374(15-16):1673–1677,2010.
[174] Zhang Q., Lu J., Lu¨ J., and Tse CK. Adaptive feedback synchronization of a general complexdynamical network with delayed nodes. IEEE Trans. Circuits Syst. II,55(2):183–187,2008.
[175] Wang Z., Wang Y., and Liu Y. Global synchronization for discrete-time stochastic complex networkswith randomly occurred nonlinearities and mixed time delays. IEEE Trsactions on Neural Networks,21(1):11–25,2010.
[176] Guo L., Nian X., and Pan H. Synchronization criteria for general coupling complex networks withtime varying delay. Control Theory&Applications,28(1):73–78,2011.
[177] Fan Y.Q., Wang Y.H., Zhang Y., and Wang Q.R. The synchronization of complex dynamicalnetworks with similar nodes and coupling time-delay. Applied Mathematics and Computation,219(12):6719–6728,2013.
[178] Lee T.H., Wu Z.G., and Park J.H. Synchronization of a complex dynamical network with couplingtime-varying delays via sampled-data control. Applied Mathematics and Computation,219(3):1354–1366,2012.
[179] Wu Z.G., Park J.H., Su H.Y., Song B., and Chu J. Exponential synchronization for complex dynam-ical networks with sampled-data. Journal of the Franklin Institute,349(9):2735–2749,2012.
[180] Guan Z.H., Yang S.H., and Yao J. Stability analysis and∞control for hybrid complex dynamicalnetworks with coupling delays. International Journal of Robust and Nonlinear Control,22(2):205–222,2012.
[181] Song Q., Cao J.D., and Liu F. Pinning-controlled synchronization of hybrid-coupled complex dy-namical networks with mixed time-delays. International Journal of Robust and Nonlinear Control,22(6):690–706,2012.
[182] Li L.X., Kurths J., Peng H.P., Yang Y.X., and Luo Q. Exponentially asymptotic synchronizationof uncertain complex time-delay dynamical networks. The European Physical Journal B,86:125,2013.
[183] Ma Q., Wang Z., and Lu J.W. Finite-time synchronization for complex dynamical networks withtime-varying delays. Nonlinear Dynamics,70(1):841–848,2012.
[184] Zhou J.P., Wang Z., Wang Y.Y., and Kong Q.K. Synchronization in complex dynamical networkswith interval time-varying coupling delays. Nonlinear Dynamics,72(1-2):377–388,2013.
[185] Rao P.C., Wu Z.Y., and Liu M. Adaptive projective synchronization of dynamical networks withdistributed time delays. Nonlinear Dynamics,67(3):1729–1736,2012.
[186] Li H.J., Wong W. K., and Tang Y. Global synchronization stability for stochastic complex dynam-ical networks with probabilistic interval time-varying delays. Journal of Optimization Theory andApplications,152(2):496–516,2012.
[187] Zhou J. and Chen T. Synchronization in general complex delayed dynamical networks. IEEETransactions on Circuits and Systems I,53(3):733–744,2006.
[188] Lu J. and Ho D.W.C. Local and global synchronization in general complex dynamical networks withdelay coupling. Chaos Solitons&Fractals,37(5):1497–1510,2008.
[189] Zhu Q. and Cao J. Adaptive synchronization of chaotic cohen-crossberg neural networks with mixedtime delays. Nonlinear Dynamics,61(3):517–534,2010.
[190] Liu Y., Wang Z., Liang J., and Liu X. Synchronization and state estimation for discrete-time complexnetworks with distributed delays. IEEE Trans. Syst. Man Cybern. B, Cybern.,38(5):1314–1325,2008.
[191] Lu¨ Y., Lu¨ W., and Sun J. Convergence dynamics of stochastic reaction-diffusion recurrent neuralnetworks with continuously distributed delays. Nonlinear Anal., Real World Appl.,9:1590–1606,2008.
[192] Liu Y., Wang Z., and Liu X. Global exponential stability of generalized recurrent neural networkswith discrete and distributed delays. Neural Netw.,19(5):667–675,2006.
[193] Liu Y., Wang Z., and Liu X. Exponential synchronization of complex networks with markovianjump and mixed delays. Physics Letters A,372:3986–3998,2008.
[194] Liu Y., Wang Z., Liang J., and Liu X. Stability and synchronization of dscrete-time markovianjumping neural networks with mixed mode-dependent time delays. IEEE Trans, on Neur. netw.,20(7):1102–1117,2009.
[195] Yang G. H. and Wang J. L. Non-fragile∞control for linear systems with multiplicative controllergain variations. Automatica,37(5):727–737,2001.
[196] Park J. H. Robust non-fragile control for uncertain discrete-delay large-scale systems with a class ofcontroller gain variations. Applied Mathematics and Computation,149(1):147–164,2004.
[197] Lien C. H., Cheng W. C., Tsai C. H., and Yu K. W. Non-fragile observer-based controls for linearsystem via approach. Chaos, Solitions and Fractals,32(4):1530–1537,2007.
[198]林瑞全，杨富文.基于∞控制理论的非脆弱控制的研究.控制与决策,19(5):598–600,2004.
[199]肖伸平，吴敏，张先明.不确定时滞系统的时滞相关非脆弱鲁棒∞控制.系统科学与数学,27(3):401–411,2007.
[200] Li X. Y. and Xing W. Non-fragile passive control for uncertain singular time-delay systems. Inter-national Journal of Information and Systems Sciences,1(3-4):390–397,2005.
[201] Keel L.H. and Bhattacharyya S.P. Robust, fragile, or optimal? IEEE Trans. on Automatic Contr.,42(8):1098–1105,1997.
[202]熊军林，张庆灵.具有结构不确定的时滞系统的最优非脆弱保成本控制.控制理论与应用,22(3):503–506,2005.
[203]付兴建，童朝南.具有时滞依赖的不确定系统鲁棒∞保代价控制.中南大学学报(自然科学版),37(1):141–144,2006.
[204] Park J. H. Delay-dependent guaranteed cost stabilization criterion for neutral delay-differential sys-tems:matrix inequality approach. Computers and Mathematics with Applications,47(10-11):1507–1515,2004.
[205] Yu Li. and Gao F. Output feedback guaranteed cost control for uncertain discrete-time systems usinglinear matrix inequalities. Journal of Optimization Theory and Applications,113(3):621–634,2002.
[206]俞立.不确定离散系统的最优保性能控制.控制理论与应用,16(5):639–642,1999.
[207]陈国定，俞立，褚健.具有状态和控制滞后不确定系统的保性能控制器设计.自动化学报,28(2):314–316,2002.
[208]俞立，冯浩.不确定离散时滞系统的保性能控制.自动化学报,27(3):392–396,2001.
[209] Yu Li, Han Qinglong, and Sun Mingxuan. Optimal guaranteed cost control of linear uncertain sys-tems with input constraints. International Journal of Control, Automation, and Systems,3(3):397–402,2005.
[210] Yu Li and Chu J. An lmi approach to guaranteed cost control of linear uncertain time-delay systems.Automatica,35(6):1155–1159,1999.
[211] Boukas E. K. Guaranteed cost control of a markov jump linear uncertain systems using a time-multiplied cost function. Journal of Optimization Theory and Application,116(1):183–204,2003.
[212] Boukas E. K. Nonfragile control design for linear markovian jumping parameters systems. Journalof Optimization Theory and Application,122(2):241–255,2004.
[213]关新平，华长春，龙承念.不确定非线性系统的鲁棒耗散性与保性能控制.控制理论与应用,20(6):938–942,2003.
[214]李俊民，张果，杜彩霞.一类不确定多输入模糊双线性系统的鲁棒∞控制.控制理论与应用,26(11):1298–1302,2009.
[215] Lee T.H., Park J.H., Ji D.H., Kwon O.M., and Lee S.M. Guaranteed cost synchronization of acomplex dynamical network via dynamic feedback control. Applied Mathematics and Computation,218(11):6469–6481,2012.
[216] Li S.K., Zhang J.X., and Tang W.S. Robust∞output feedback control for uncertain complexdelayed dynamical networks. Computers&Mathematics with Applications,62(1):497–505,2011.
[217] Park J. H. Robust guaranteed cost control for uncertain linear differential systems of neural type.Appl Mathematics and Computation,140(2-3):523–535.,2003.
[218] Foda S. G. and Mahmoud M. S. Adaptive stabilization of delay differential systems with unknownuncertainty bounds. Int. J. Control,71(2):259–275,1998.
[219] Magdi S. M., El-Ke′bir B., and Abdulla I. Robust adaptive control of uncertain discrete-time state-delay systems. Computers and Mathematics with Application,55(12):2887–2902,2008.
[220]熊军林，张庆灵.结构不确定离散系统的最优非脆弱保成本控制.控制理论与应用,21(2):279–282,2004.
[221] Wang L., Dai H. Dong H., Shen Y., and Sun Y. Adaptive synchronization of weighted complexdynamical networks with coupling time-varying delays. Phys. Lett. A,372(20):3632–3639,2008.
[222]王磊，戴华平，孙优贤.时变复杂动力学网络的同步控制.控制理论与应用,25(4):603–607,2008.
[223] Magdi S. M. Resilient control of uncertain dynamical system. Berlin: Springer-Verlag,2004.
[224]陈国培，李俊民，杨莹.一类不确定脉冲混合系统的非脆弱控制器设计.西安电子科技大学学报,35(1):65–70,2008.
[225] Zhang Guo and Li Junmin. Non-fragile guaranteed cost control of discrete-time fuzzy bilinearsystem. Journal of Systems Engineering and Electronics,21(4):629–634,2010.
[226] Kun Ji and Dong Wei. Resilient control for wireless networked control systems. InternationalJournal of Control, Automation, and Systems,9(2):285–293,2011.
[227]李俊民，曹梦涛，沈思.时变复杂动态网络非脆弱同步算法.西安电子科技大学学报(自然科学版),39(5):156–164,2012.
[228] Wang Z., Liu Y., Li M., and Liu X. Stability analysis for stochastic cohen-grossberg neural networkswith mixed time delays. IEEE Transactions on Neural Networks,17(3):814–821,2006.
[229] Liu Y., Wang Z., and Liu X. Robust stability of discrete-time stochastic neural networks with time-varying delays. Neurocomputing,71:823–833,2008.
[230] Weir G., Wang Z., Lam J., Fraser K., Rao G., and Liu X. Robust filtering for stochastic geneticregulatory networks with time-varying delay. Mathematical Biosciences,220:73–80,2009.
[231] Liu Y., Wang Z., and Liu X. Robust∞filtering for discrete nonlinear stochastic systems withtime-varying delay. J. Math. Anal. Appl.,341:318–336,2008.
[232] Liang J., Wang Z., and Liu X. Exponential synchronization of stochastic delayed discrete-timecomplex networks. Nonlinear Dyn,53:153–165,2008.
[233] Li C., Chen L., and Aihara K. Stochastic synchronization of genetic oscillator networks. BMCSystems Biology,1:1–6,2007.
[234] Wang Y., Wang Z., and Liang J. Global synchronization for delayed complex networks with ran-domly occurring nonlinearities and multiple stochastic disturbances. J. Phys. A: Math. Theor.,42(13):135101,2009.
[235] Li H. and Yue D. Synchronization of markovian jumping stochastic complex networks with dis-tributed time delays and probabilistic interval discrete time-varying delays. J. Phys. A: Math. Theor.,43(10):105101,2010.
[236] Liang J., Wang Z., and Liu X. State estimation for coupled uncertain stochastic networks with mss-ing measurements and time-varying delays: The discrete-time case. IEEE Transactions on NeuralNetworks,20(5):781–794,2009.
[237] Ma L., Wang Z., Hu J., Bo Y., and Guo Z. Robust variance-constrained filtering for a class ofnonlinear stochastic systems with missing measurements. Signal Processing,90(6):2060–2071,2010.
[238] Gao H., Meng X., Chen T., and Lam J. Stabilization of networked control systems via dynamicoutput-feedback controllers. SIAM J. Control Optim,48(5):3643–3658,2010.
[239] Belykh I. V., Belykh V. N., and Hasler M. Blinking model and synchronization in small-worldnetworks with a time-varying coupling. Physica D,195(1-2):188–206,2004.
[240] Atay F. M., Biyikoglu T., and Jost J. Network synchronization: Spectral versus statistical properties.Physica D,224(1-2:5–41,2006.
[241] Yu W., Cao J., and Yuan K. Synchronization of switched system and application in communication.Phys. Lett. A,372:4438–4445,2008.
[242] Cao J., Wang Z., and Sun Y. Synchronization in an array of linearly stochastically coupled networkswith time delays. Phys. A,385(2):718–728,2007.
[243] Yang X. and Cao J. Stochastic synchronization of coupled neural networks with intermittent control.Phys. Lett. A,373:3259–3272,2009.
[244] Yu W. W., Chen G., and Cao J. D. Adaptive synchronization of uncertain coupled stochastic complexnetworks. Asian Journal of Control,13(3):418–429,2011.
[245] Yi J., Wang Y., Xiao J., and Huang Y. Exponential synchronization of complex dynamical networkswith markovian jump parameters and stochastic delays and its application to multi-agent systems.Commun. Nonlinear Sci. Numer. Simulat.,18(5):1175–1192,2013.
[246] Lee T.H., Ji D.H., Park J.H., and Jung H.Y. Decentralized guaranteed cost dynamic control forsynchronization of a complex dynamical network with randomly switching topology. Applied Math-ematics and Computation,219(3):996–1010,2012.
[247] Yang X. and Cao J. Finite-time stochastic synchronization of complex networks. Applied Mathe-matical Modelling,34:3631–3641,2010.
[248] Tang Y., Wong W. K., Fang J. A., and Miao Q. Y. Pinning impulsive synchronization of stochasticdelayed coupled networks. Chin. Phys. B,20(4):040513,2011.
[249] Tu L. Global synchronization of general delayed complex networks with stochastic disturbances.Chin. Phys. B,20(3):030504,2011.
[250] Yang Z. Q., Liu Z. X., Chen Z. Q., and Yuan Z. Z. Controlled synchronization of complex networkwith different kinds of nodes. J. Control Theory Appl,6(1):11–15,2008.
[251] Chen J. R., Jiao L. C., Wu J. S., and Wang X. H. Adaptive synchronization between two differentcomplex networks with time-varying delay coupling. Chinese Physics Letters,26(6):060505,2009.
[252] Zhang G., Zhang W., and Liu Z. R. Synchronization of coupled nonidentical dynamical systems.Chin. Phys.Lett.,27(3):030504,2010.
[253] Wu J. S., Jiao L. C., and Chen G. R. Cluster synchronization in a network of non-identical dynamicsystems. Chin. Phys. B,20(6):060503,2011.
[254] Kolmanovskii V. B. and Myskis A. D. Introduction to the Theory and Applications of FunctionalDifferential Equations. Dordrecht: Kluwer Academic Publishers,1999.
[255] Mao X. Stochastic Differential Equations and Appli-cations. Chichester: Horwood Pubishing,1997.
[256]廖晓昕.动力系统的稳定性理论和应用.北京:国防工业出版社,2000.
[257] Mandelbrot B. B. and Van Ness J. W. Fractional brownian motions, fractional noises and applica-tions. SIAM Review,10(4):422–437,1968.
[258] Oldham K.B and Spanier J. The fractional calculus: theory and applications of differentiation andintegration to arbitrary order. New York and London: Academic Press,1974.
[259]李岩.分数阶微积分及其在粘弹性材料和控制理论中的应用. PhD thesis,济南:山东大学,2008.
[260] West B.J., Bolognab M., and Grigolini P. Physics of fractal operators. NewYork: Springer,2003.
[261] Zalavsky G.M. Chao,fractional kinctics and anomalous transport. Phys.Rcp,371:461–580,2002.
[262] Chengbin M. and Yoichi H. First generation crone control. In Proceedings of the InternationalConference on Systems Engineering in the Service of Humans, volume2, pages130–135,1993.
[263] Oustaloup A. and Bluteau B. Fractional order control and its application of controller forrobust two-inertia speed control. In Proceedings of The4th International Conference on PowerElectronics and Motion Control, volume3, pages1477–1482,2004.
[264] Podlubny I. Fractional differential equations. New York: Academic Press,1999.
[265] Wu X.J., Lai D.R., and Lu H.T. Generalized synchronization of the fractional-order chaos in weight-ed complex dynamical networks with nonidentical nodes. Nonlinear Dynamics,69(1-2):667–683,2012.
[266] Wong W.K., Li H., and Leung S.Y.S. Robust synchronization of fractional-order complex dynamicalnetworks with parametric uncertainties. Commun Nonlinear Sci Numer Simulat,17:4877–4890,2012.
[267] Chen L., Chai Y., Wu R., Sun J., and Ma T. Cluster synchronization in fractional-order complexdynamical networks. Physics Letters A,376:2381–2388,2012.
[268] Chai Y., Chen L., Wu R., and Sun J. Adaptive pinning synchronization in fractional-order complexdynamical networks. Physica A,391:5746–5758,2012.
[269] Butzer P.L. and Westphal U. An Introduction to Fractional Calculus. Singapore: World Scientific,2000.
[270] Caputo M. Linear models of dissipation whose q is almost frequency independent-ii. GeophysicalJournal Royal Astronomical Society,13(5):529–539,1967.
[271] Keil F., Mackens W., and Werther J. Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties. Heidelberg:Springer-Verlag,1999.
[272]张凤荣.分数阶微分系统的稳定性分析. PhD thesis,上海:上海大学,2011.
[273] Diethelm K., Ford N.J., and Freed A.D. A predictor-corrector approach for the numerical solutionof fractional differential equations. Nonlinear Dynamics,29(1-4):3–22,2002.
[274] Matignon D. Stability results for fractional differential equations with applications to control pro-cessing. In Computational engineering in systems applications multiconference, proceeeding ofIMACS, IEEE-SMC, Lille, France, pages963–968,1996.
[275]秦昌茂，齐乃明，朱凯.分数阶系统变阶次状态空间建模及稳定理论.控制与决策,26(11):1757–1760,2011.
[276] Hu J. B., Han Y., and Zhao L. D. A novel stability theorem for fractional systems and its applying insynchronizing fractional chaotic system based on back-stepping approcach. Acta Phys Sin,58:2235–2239,2009.
[277] Li C. and Chen G. Chaos in the fractional order chen system and its control. Chaos Solitons&Fractals,22(3):549–554,2004.
[2] Watts D.J. and Strogatz S.H. Collective dynamics of”small-world” networks. Nature,393:440–442,1998.
[3] Baraba′si A.L. and Albert R. Emergence of scaling in random networks. Science,286(10):509–512,1999.
[4] Jeong H., Tombor B., Albert R., Oltvai Z. N., and Baraba′si A.L. The large-scale organization ofmetabolic networks. Nature,407:651–654,2000.
[5] Ebel H., Mielsch L., and Bornholdt S. Scale-free topology of e-mail networks. Physical Review E,66(3):035103,2002.
[6] Li W. and Cai X. Statistical analysis of airport network of china. Physical Review E,69(4):046106,2004.
[7] Boccaletti S., Latora V., Moreno Y., Chavez M., and Hwang D.U. Complex networks: structure anddynamics. Physics Reports,424(4-5):175–308,2006.
[8] Bond J. and Murty U.S.R. Groph Theory with Applications. London and Basingstoke, MacMillanPress LTD,1976.
[9] Xu J. M. Topological Structure and Analysis of Interconnection Network. London, Kluwer AeademicPublishers,2001.
[10] Erdo¨s P. and Re′nyi A. On random graphs. Published in Math Debrecen,1959.
[11] Erdo¨s P. and Re′nyi A. On the evolution of random graphs. Publications of the Mathematical Instituteof the Hungarian Academy of Science,5(1):17–61,1960.
[12] Erdo¨s P. and Re′nyi A. On the strength of connectedness of a random graph. Acta MathematicaScientia Hungary,12:261–267,1961.
[13] Bolloba′s B. Random Graphs. New York, Academic Press,2001.
[14] Strogatz S. H. Exploring complex networks. Nature,410:268–276,2001.
[15] Albert R. and Baraba′si A. L. Statistical mechanics of complex networks. Reviews of Modern Physics,74(1):47–97,2002.
[16] Wang W. X., Wang B.H., Hu B., Yan G., and Ou Q. General dynamics of topology and traffic onweighted technological networks. Physical Review Letters,95(18):188702,2005.
[17]方锦清，李永.网络科学中统一混合理论模型的若干研究进展.力学进展,38(6):663–678,2008.
[18]刘宏鲲，张效莉，曹莨，汪秉宏，周涛.中国城市航空网络航线连接机制分析.中国科学G辑,39(7):935–942,2009.
[19] Wu C.W. Synchronization in complex networks of nonlinear dynamical systems. Singapore: WorldScientific,2007.
[20] Diaz-Guilera A. Kurths J. Moreno Y. Zhou C. Arenas, A. Synchronization in complex networks.Physics Reports,469(3):93–153,2008.
[21]赵明，周涛，陈关荣，汪秉宏.复杂网络上动力系统同步的研究进展―如何提高网络的同步能力.物理学进展,28(1):22–34,2008.
[22] Sun Y.G. and Wang L. Consensus problems in networks of agents with double-integrator dynamicsand time-varying delays. International Journal of Control,82(10):1937–1945,2009.
[23] Vespignani A. Complex networks: The fragility of interdependency. Nature,464:984–985,2010.
[24] Buldyrev S.V., Parshani R., Paul G., Stanley H.E., and Havlin S. Catastrophic cascade of failures ininterdependent networks. Nature,464:1025–1028,2010.
[25] Li X., Wang X. F., and Chen G. Pinning a complex dynamical network to its equilibrium. IEEETrans. on Circuits and Systems I,51(10):2074–2087,2004.
[26]汪小帆，李翔，陈关荣.复杂网络理论及其应用.北京：清华大学出版社,2006.
[27] Newman M E J. and Watts D.J. Renormalization group analysis of the small-world network model.Physics Letters A,263(4-6):341–346,1999.
[28]赵明.复杂网络上动力系统同步现象的研究. PhD thesis,合肥:中国科学技术大学,2007.
[29] Pecora L.M. and Carroll T.L. Master stability functions for synchronized coupled systems. PhysicalReview Letters,80(10):2109–2112,1998.
[30] Wang X.F. Complex networks: topology, dynamics and synchronization. International Journal ofBifurcation&Chaos,12(5):885–916,2002.
[31] Wang X.F. and Chen G. Synchronization in small-world dynamical networks. International Journalof Bifurcation&Chaos,12(1):187–192,2002.
[32] Barahona M. and Pecora L.M. Synchronization in small-world systems. Physical Review Letters,89(5):054101,2002.
[33] Hu G., Yang J., and Liu W. Instability and controllability of linearly coupled oscillators: Eigenvalueanalysis. Physical Review E,58(4):4400–4453,1998.
[34] Zhao J., Hall D. J., and Liu T. Synchronization of dynamical networks with nonidentical nodes:Criteria and control. IEEE Transactions on Circuits and Systems I,58(3):584–594,2011.
[35] Chen Y., Rangarajan G., and M. Ding. General stability analysis of synchronized dynamics incoupled systems. Physical Review E,67(4):026209,2003.
[36] Belykh V., Belykh I., and Hasler M. Connection graph stability method for synchronized coupledchaotic systems. Physica D,195(1-2):159–187,2004.
[37] Lu W. and Chen T. New approach to synchronization analysis of linearly coupled ordinary diffrentialsystems. Physica D,213(2):214–230,2006.
[38] Chen T. and Zhu Z.M. Exponential synehronization of nonlinear coupled dynamical networks.International Journal of Bifurcation&Chaos,17(3):999–1005,2007.
[39] Leyva I., Sendina-Nadal I., Almendral J. A., and Sanjnan M. A. F．. Sparse repulsive couplingenhances synchronization in complex networks. Physical Review E,74:056112,2006.
[40] Stilwell D. J., Bollt E., and Roberson D. Sufficient conditions for fast switching synchronizationin time-varying network topologies. SIAM Journal on Applied Dynamical System,5(1):140–156,2006.
[41] Lu¨ J. and Chen G. A time-varying complex dynamical network model and its controlled synchro-nization criteria. IEEE Transactions on Automatic Control,50(6):841–846,2005.
[42] Lu¨ J., Yu X., and Chen G. Chaos synchronization of general dynamical networks. Physica A,334(1-2):281–302,2004.
[43] Boccaletti S., Hwang D. U., Chavez M., Amann A., Kurths J., and Pecora M. Synchronization indynamical networks：evolution along commutative graphs. Physical Review E,74:016102,2006.
[44] Ito J. and Kaneko K. Spontaneous structure formation in a network of chaotic units with variableconnection strengths. Physical Review Letters,88(2):028701,2001.
[45] Zanette D. H. and Mikhailov A. S. Dynamical systems with time-dependent coupling：clusteringand critical behavior. Physica D,194(3-4):203–218,2004.
[46] Porfiri M., Stilwell D. J., Bollt E. M., and Skufca J. D. Random talk: Random walk and synchroniz-ability in a moving neighborhood network. Physica D,224(1-2):102–113,2006.
[47] Jadbabaie A., Lin J., and Morse A. S. Coordination of groups of mobile autonomous agents usingnearest neighbor rules. IEEE Transactions on Automatic Control,48:988–1001,2003.
[48] Ogren P., Fiorelli E., and Leonard N. E. Cooperative control of mobile sensor networks：adaptivegradient climbing in a distributed environment. IEEE Transactions on Automatic Control,49:1292–1302,2004.
[49] Moreau L. Stability of multi-agent systems with time-dependent communication links. IEEE Trans-actions on Automatic Control,50:169–182,2005.
[50] Xiao F. and Wang L. State consensus for multi-agent systems with switching topologies and time-varying delays. International Journal of Control,79:1277–1284,2006.
[51] Xie G. and Wang L. Consensus control for a class of networks of dynamic agents. InternationalJournal of Robust Nonlinear Control,17:941–959,2007.
[52] Hong Y., Hua J., and Gao L. Lyapunov-based approach to multi-agent systems with switching jointlyconnected interconnection. IEEE Transactions on Automatic Control,52:943–948,2007.
[53] Frasca M., Buscarino A., Rizzo A., Fortuna L., and Boccaletti S. Synchronization of moving chaoticagents. Physical Review Letters,100:044102,2008.
[54] Buscarino A., Fortuna L., and Frasca M. Dynamical network interactions in distributed control ofrobots. Chaos,16:015116,2006.
[55] Dan S., S rensen P. G., and Hynne F. Sustained oscillations in living cells. Nature,402:320–322,1999.
[56] Dan S., Hynne F., and Monte S. D. Synchronization of glycolitic oscillations in intact yeast cells.Faraday Discuss,120:261–276,2001.
[57] Lu¨ J.H. and Chen G. A time-varying complex dynamical network model and its controlled synchro-nization criteria. IEEE Transactions on Automatic Control,50(6):841–846,2005.
[58] Daniel J. S., Erik M. B., and Roberson D. G. Synchronization of time-varying networks under fastswitching. In Proceedings of the2006American Control Conference,2006.
[59] Belykh I. V., Hasler M., Laurent M., and Nijmeijer. Psynchronization and graph topology. Interna-tional Journal of Bifurcation and Chaos,15(11):3423–3433,2005.
[60] Belykh I., Belykh V., and Hasler M. Generalized connection graph method for synchronization inasymmetrical networks. Physica D,224(1-2):42–51,2006.
[61] Chen M. Y. Synchronization in time-varying networks：a matrix measure approach. PhysicalReview E,76:016104,2007.
[62] Zhang R., Hu M., and Xu Z. Synchronization in complex networks with adaptive coupling. Phys.Lett. A,368(8):276–280,2007.
[63] Li Z., Jiao L., and Lee J.J. Robust adaptive global synchronization of complex dynamical networksby adjusting time-varying coupling strength. Physica A,387(5-6):1369–1380,2008.
[64] Liu H., Chen J., Lu J., and Cao M. Generalized synchronization in complex dynamical networks viaadaptive couplings. Physica A,389(8):1759–1770,2010.
[65] Lu J. and Cao J. Adaptive synchronization of uncertain dynamical networks with delayed coupling.Nonlinear Dynamics,53(1-2):107–115,2008.
[66] Yeung M. K. S. and Strogatz S. H. Time delay in the kuramoto model of coupled oscillators. PhysicalReview Letters,82(3):648–651,1999.
[67] Heil T., Fischer I., and Elsasser W. Chaos synchronization and spontaneous symmetry-breaking insymmetrically delay-coupled semiconductor lasers. Physical Review Letters,86(5):795–798,2001.
[68] Strogatz S. H. Death by delay. Nature,394:316–317,1998.
[69] Reddy D. V. R., Sen A., and Johnston G. L. Time delay induced death in coupled limit cycleoscillators. Physical Review Letters,80(23):5109–5112,1998.
[70] Niebur E., Schuster H. G., and Kammen D. M. Collective frequencies and metstability in networksin limit-cycle oscillators with time delay. Physical Review Letters,67(20):2753–2756,1991.
[71] Li C. and Chen G. Sychronization in general complex dynamical networks with coupling delays.Physica A,343:263–278,2004.
[72] Gao H., Lam J., and Chen G. New criteria for synchronization stability of general complex dynam-ical networks with coupling delays. Phys. Lett. A,360(2):263–273,2006.
[73] Wang Q., Chen G., Lu Q., and Hao F. Novel criteria of synchronization stability in complex networkswith coupling delays. Physica A,378(2):527–536,2007.
[74] Li C. P., Sun W. G., and Kurths J. Synchronization of complex dynamical networks with time delays.Physica A,361(1):24–34,2006.
[75] Li P., Yi Z., and Zhang L. Global synchronization of a class of delayed complex networks.Chaos，Solitons&Fractals,30(4):903–908,2006.
[76] Lu W., Chen T., and Chen G. Synchronization analysis of linearly coupled systems described bydiffrential equations with a coupling delay. Physica D,221(2):118–134,2006.
[77] Liu X. and Chen T. P. Exponential synchronization of nonlinear coupled dynamical networks with adelayed coupling. Physica A,381:82–92,2007.
[78] Liu B., Teo K. L., and Liu X. Global synchronization of dynamical networks with coupling timedelays. Physics Letters A,368(1-2):53–63,2007.
[79] Wang L., Dai H. P., and Sun Y. X. Synchronization criteria for a generalized complex delayeddynamical network model. Physica A,383(2):703–713,2007.
[80] Zhou J., Xiang L., and Liu Z. R. Synchronization in complex delayed dynamical networks withimpulsive effects. Physica A,384(2):684–692,2007.
[81] Zhou J., Xiang L., and Liu Z. R. Global synchronization in general complex delayed dynamicalnetworks and its applications. Physica A,385(2):729–742,2007.
[82] Yang M., Wang Y., and Wang K. Delay independent synchronization of complex network via hybridcontrol. In ACC’08, pages2266–2271,2008.
[83] Cai S., Zhou J., Xiang L., and Liu Z. Robust impulsive synchronization of complex delayed dynam-ical networks. Phys. Lett. A,372(30):4990–4995,2008.
[84] Chen G R，Zhou J，Liu Z R．. Global synchronization of coupled delayed neural networks andapplications to chaotic cnn model. International Journal of Bifurcation and Chaos,14(7):2229–2240,2004.
[85] Lu W. L. and Chen T. P. Synchronization of coupled connected neural networks with delays. IEEETransactions Circuits System-I,51(12):2491–2503,2004.
[86] Wang W. and Cao J. Synchronization in an array of linearly coupled networks with time-varyingdelay. Physica A,366(1):197–211,2006.
[87] Sun Y., Cao J., and Wang Z. Exponential synchronization of stochastic perturbed chaotic delayedneural networks. Neurocomputing,70(13-15):2477–2485,2007.
[88] Hua C., Wang Q., and Guan X. Global adaptive synchronization of complex networks with nonlineardelay coupling interconnections. Physics Letters A,368(3-4):281–288,2007.
[89] Li Z., Feng G., and Hill D. Controlling complex dynamical networks with coupling delays to adesired orbit. Phys. Lett. A,359(1):42–46,2006.
[90] Lu J. Q., Ho D. W. C., and Liu M. Globally exponential synchronization in an array of asymmetriccoupled neural networks. Physics Letters A,369(5-6):444–451,2007.
[91] Liu T., Dimirovski G. M., and Zhao J. Exponential synchronization of complex delayed dynamicalnetworks with general topology. Physica A,387(2-3):643–652,2008.
[92] Wu J. and Jiao L. Synchronization in dynamic networks with nonsymmetrical time-delay couplingbased on linear feedback controllers. Physica A,387(8-9):2111–2119,2008.
[93]罗群，吴薇，李丽香，杨义先，彭海朋.节点含时滞的不确定复杂网络的自适应同步研究.物理学报,57(3):1529–1534,2008.
[94] Yu W., Cao J., and Lu J. Global synchronization of linearly hybrid coupled networks with time-varying delay. SIAM Journal on Applied Dynamical Systems,7(1):108–133,2008.
[95] Dai Y., Cai Y., and Xu X. Synchronization criteria for complex dynamical networks with neutral-type coupling delay. Physica A,387(18):4673–4682,2008.
[96] He Y., Wu M., She J.H., and Liu G.P. Delay-dependent robust stability criteria for uncertain neutralsystems with mixed delays. Systems&Control Letters,51(1):57–65,2004.
[97] Yao J., Wang H.O., Guan Z.H., and Xu W. Passive stability and synchronization of complex spatio-temporal switching networks with time delays. Automatica,45(7):1721–1728,2009.
[98] Yue D. and Li H. Synchronization stability of continuous/discrete complex dynamical networks withinterval time-varying delays. Neurocomputing,73(4-6):809–819,2010.
[99] Wang X. and Chen G. Synchronization in small-world dynamical net-works. International Journalof Bifurcation and Chaos,12(1):187–192,2002.
[100] Wang X. and Chen G. Synchronization in scale-free dynamical net-works: robustness and fragility.IEEE Trans. on Circuits and Systems I,49(1):54–62,2002.
[101] Gu Z.M., Zhao M., Zhou T., Zhu C.P., and Wang B.H. Phase synchronization of non-abelian oscil-lators on small-world networks. Physics Letters A,362(2-3):115–119,2007.
[102] Fumito M. and Takashi O. Synchronization of coupled oscillators on small-world networks. PhysicaD,238(14):1180–1185,2009.
[103] Zou Y. and Chen G. Choosing effective controlled nodes for scale-free network synchronization.Physica A,388(14):2931–2940,2009.
[104] Sorrentino F., di Bernardo M., Huerta Cue′llar G., and Boccaletti S. Synchronization in weightedscale-free networks with degree-degree correlation. Physica D,224(1-2):123–129,2006.
[105] Duan Z., Chen G., and Huang L. Synchronization of weighted networks and complex synchronizedregions. Physics Letters A,372(21):3741–3751,2008.
[106] Wu X. and Lu H. Exponential synchronization in delayed and non-delayed coupling dynamicalnetworks. Computers and Mathematics with Applications,60(8):2476–2487,2010.
[107] Li C., Sun W., and Kurths J. Synchronization between two coupled complex networks. PhysicalReview E,76(4):046204,2007.
[108] Wu X. and Lu H. Cluster synchronization in the adaptive complex dynamical networks via a novelapproach. Physics Letters A,375(14):1559–1565,2011.
[109] Liu H., Lu J.A., Lu¨ J., and Hill D.J. Structure identification of uncertain general complex dynamicalnetworks with time delay. Automatica,45(8):1799–1807,2009.
[110] Tang Y., Wang Z., and Fang J. Pinning control of fractional-order weighted complex networks.Chaos,19(1):013112,2009.
[111] Tang Y. and Fang J. Synchronization of n-coupled fractional-order chaotic systems with ring con-nection. Commun. Nonlinear Sci. Numer. Simulat.,15(2):401–412,2010.
[112] Wang J. and Zhang Y. Network synchronization in a population of star-coupled fractional nonlinearoscillators. Phys. Lett. A,374(13-14):1464–1468,2010.
[113] Wu X. and Lu H. Outer synchronization of two different fractional-order complex dynamical net-works. Chinese Physics B.,19(7):070511,2010.
[114] Hu G. and Qu Z. L. Controlling spatiotemporal chaos in coupled map lattice systems. PhysicalReview Letters,72(1):68–71,1994.
[115] Wang X. and Chen G. Pinning control of scale-free dynamical networks. Phycica A,310(3-4):521–531.,2002.
[116] Fan Z. and Chen G. Pinging control of scale-flee complex networks. IEEE International Symposiumon Circuits and Systems，Kobe，Japan,1:284–287,2005.
[117] Liu Z., Chen Z., and Yuan Z. Pinning control of weighted general complex dynamical networks withtime delay. Physica A,375(1):345–354,2007.
[118] Chen T., Liu X., and Lu W. Pinning complex networks by a single controller. IEEE Trans. CircuitsSyst. I,54(6):1317–1326,2007.
[119] Feng J.W., Sun S.H., Xu C., Zhao Y., and Wang J.Y. The synchronization of general complexdynamical network via pinning control. Nonlinear Dynamics,67(2):1623–1633,2012.
[120] Porfiri M. and Bernardo M. D. Criteria for global pinning-controllability of complex networks.Automatics,44(12):3100–3106,2008.
[121] Zhou J., Lu J. A., and Lu¨ J. H. Pinning adaptive synchronization of a general complex dynamicalnetwork. Automatica,44(4):996–1003,2008.
[122] Guo W., Austin F. Chen S., and Sun W. Pinning synchronization of the complex networks withnon-delayed and delayed coupling. Physics Letters A,373(17):1565–1572,2009.
[123] Ma Q. and Lu J. Cluster synchronization for directed complex dynamical networks via pinningcontrol. Neurocomputing,101(4):354–360,2013.
[124] Su H.S., Rong Z.H., Chen M.Z.Q., Wang X.F., Chen G.R., and Wang H.W. Decentralized adaptivepinning control for cluster synchronization of complex dynamical networks. IEEE Transactions onCybernetics,43(1):394–399,2013.
[125] Xiong W., Ho D. W. C., and Huang C. Pinning synchronization of time-varying polytopic directedstochastic networks. Physics Letters A,374(3):439–447,2010.
[126]姚静，关治洪.拓扑切换网络的脉冲控制.复杂系统与复杂性科学,2(2):24–29,2005.
[127] Yao J., Guan Z. H., and Hill DV Wang H O. On passivity and impulsive control of complex dynam-ical networks with coupling delays. In Proceeding of the44m IEEE conference on Decision andcontrol．and the European Control Conference2005, pages1595–1600,2005.
[128] Guan Z. H. and Zhang H. Stabilization of complex network with hybrid impulsive and switchingcontrol. Chaos，Solitons&Fractals,37(5):1372–1382,2008.
[129] Liu B., Liu X. Z., Chen G., and Wang H. Y. Robust impulsive synchronization of uncertain dynam-ical networks. IEEE Transactions on Circuits&Systems I,52(2):1431–1441,2005.
[130] Ma Z J．Zhang G，Liu Z R. Synchronization of complex dynamical networks via impulsive con-trol. Chaos,17(4):043126,2007.
[131] Li P., Cao J., and Wang Z. Robust impulsive synchronization of coupled delayed neural networkswith uncertainties. Physica A,373(1):261–272,2007.
[132] Zhou J., Q.J. Wu, and Xiang L. Pinning complex delayed dynamical networks by a single impulsivecontroller. IEEE Transactions on Circuits and Systems I,58(12):2882–2893,2011.
[133] Yang Y. Q. and Cao J. D. Exponential lag synchronization of a class of chaotic delayed neuralnetworks with impulsive effects. Physica A,386(1):492–502,2007.
[134] Jiang H. B. Hybrid adaptive and impulsive synchronisation of uncertain complex dynamical net-works by the generalised barbalat’s lemma. IET Control Theory&Applications,3(10):1330–1340,2009.
[135] Huang D. B. Simple adaptive-feedback controller for identical chaos synchronization. PhysicalReview E,71(3):037203,2005.
[136] Sun M., Zeng C. Y., and Tian L. X. Projective synchronization in drive-response dynamical networksof partially linear systems with time-varying coupling delay. Physics Letters A,372(46):6904–6908,2008.
[137] Wen S., Chen S., and Guo W. Adaptive global synchronization of a general complex dynamicalnetwork with non-delayed and delayed coupling. Phys. Lett. A,372(42):6340–6346,2008.
[138] Wang K., Teng Z. D., and Jiang H. J. Adaptive synchronization of neural networks with time-varyingdelay and distributed delay. Physica A,387()2-3:631–642,2008.
[139] Li Z. and Chen G. Robust adaptive synchronization of uncertain dynamical networks. Phys. Lett. A,324(2-3):166–178,2004.
[140] Zhou J., Lu J., and Lu¨ J. Adaptive synchronization of an uncertain complex dynamical network.IEEE Trans. on Automatic Control,51(4):652–656,2006.
[141] Chen M. Y. and Zhou D. H. Synchronization in uncertain complex networks. Chaos,16(1):013101,2006.
[142] Lu W. L. Adaptive dynamical networks via neighborhood information：synchronization and pin-ning control. Chaos,17(2):023122,2007.
[143] Li K., Small M., and Fu X. Generation of clusters in complex dynamical networks via pinningcontrol. Journal of Physics A：Mathematical and General,41:505101,2008.
[144] Wu X. Synchronization-based topology identification of weighted general complex dynamical net-works with time-varying coupling delay. Physica A,387(4):997–1008,2008.
[145] Zheng S., Bi Q., and Cai G. Adaptive projective synchronization in complex networks with time-varying copling delay. Physics Letters A,373(17):1553–1559,2009.
[146] Zhou J. and Lu J. A. Topology identification of weighted complex dynamical networks. Physica A,386(1):481–491,2007.
[147]张青，杨正全，陈增强.带有未知参数的复杂动态网络的自适应同步(英文).南开大学学报(自然科学版),43(4):7–14,2010.
[148] Xiao X. Y., Xu W., Li X. C., and Tang S. F. Adaptive complete synchronization of chaotic dynamicalnetwork with unknown and mismatched parameters. Chaos,17(3):033118,2007.
[149] Yu W. W. and Cao J. D. Adaptive synchronization and lag synchronization of uncertain dynamicalsystem with time delay based on parameter identification. Physica A,375(2):467–482,2007.
[150] Mahdavi N., Menhaj M.B., Kurths J., and Lu J. Fuzzy complex dynamical networks and its syn-chronization. IEEE Transactions on Cybernetics,43(2):648–659,2013.
[151]卢文联.动力系统与复杂网络：理论与应用. PhD thesis,上海：复旦大学,2005.
[152] Arenas A., Diaz-Guilera A., Kurths J., Moreno Y., and Zhou C. Synchronization in complex net-works. Physics Reports,469(3):93–153,2008.
[153] Pecora L.M. and Carroll T.L. Master stability functions for synchronized coupled systems. PhysicalReview Letters,80(10):2109–2112,1998.
[154] Du H., Shi P., and Lu¨ N. Function projective synchronization in complex dynamical networks withtime delay via hybrid feedback control. Nonlinear Analysis: Real World Applications,14(2):1182–1190,2013.
[155] Ma Z.J., Liu Z.R., and Zhang G. A new method to realize cluster synchronization in connectedchaotic networks. Chaos,16(2):023103,2006.
[156] Wu W., Zhou W., and Chen T. Cluster synchronization of linearly coupled complex networks underpinning control. IEEE Trans. on Circuits and Systems I,56(4):829–839,2009.
[157] Zhao J.C., Aziz-Alaoui M. A., and Bertelle C. Cluster synchronization analysis of complex dynam-ical networks by input-to-state stability. Nonlinear Dynamics,70(2):1107–1115,2012.
[158] Yu L., Tu L.L., and Liu H.F. Adaptive cluster synchronization for a complex dynamical networkwith delays and stochastic perturbation. The European Physical Journal B,86:130,2013.
[159] Kaneko K. Relevance of clustering to biological networks. Physica D,75:55–73,1994.
[160] Belykh I., Belykh V., Nevidin K., and Hasler M. Persistent clusters in lattices of coupled nonidenticalchaotic systems. Chaos,13(1):165–178,2003.
[161] Cao J. and Li L. Cluster synchronization in an array of hybrid coupled neural networks with delay.Neural Networks,22(4):335–342,2009.
[162] Newman M.E.J. The structure and function of complex networks. SIAM Review,45(2):167–256,2003.
[163] Wu C. Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling. IEEE Trans. Circuits Syst. II,52(5):282–286,2005.
[164] Li Z., Jiao L., and Lee J. Robust adaptive global synchronization of complex dynamical networksby adjusting time-varying coupling strength. Physica A,387(5-6):1369–1380,2008.
[165] Wang Y.H., Fan Y.Q., Wang Q.Y., and Zhang Y. Stabilization and synchronization of complex dy-namical networks with different dynamics of nodes via decentralized controllers. IEEE Transactionson Circuits and Systems I,59(8):1786–1795,2012.
[166] Guo W., Chen S., and Sun W. Topology identification of the complex networks with non-delayedand delayed coupling. Phys. Lett. A,373(41):3724–3729,2009.
[167] Xu Y., Zhou W., Fang J., Sun W., and Pan L. Topology identification and adaptive synchronizationof uncertain complex networks with non-derivative and derivative coupling. Journal of the FranklinInstitute,347(4):1566–1576,2010.
[168] Song Y., Yu X., Chen G., Xu J., and Tian Y. Time delayed repetitive learning control for chaoticsystems. Int. J. Bifur. Chaos,12(5):1057–1066,2002.
[169] Xu J. and Yan R. On repetitive learning control for periodic tracking tasks. IEEE Trans. Autom.Control,51(11):1842–1848,2006.
[170] Tao G. A simple alternative to the barbalat lemma. IEEE Transactions on Automatic Control,42(5):698–698,1997.
[171] Sun M. A barbalat-like lemma with its application to learning control. IEEE Transactions onAutomatic Control,54(9):2222–2225,2009.
[172] Guo X.，Li J. Projective synchronization of complex dynamical networks with time-varying cou-pling strength via hybrid feedback control. Chinese Physics Letters,28(12):120503,2011.
[173] Xu Y., Zhou W., Fang J., and Sun W. Adaptive synchronization of the complex dynamical networkwith non-derivative and derivative coupling. Phys. Lett. A,374(15-16):1673–1677,2010.
[174] Zhang Q., Lu J., Lu¨ J., and Tse CK. Adaptive feedback synchronization of a general complexdynamical network with delayed nodes. IEEE Trans. Circuits Syst. II,55(2):183–187,2008.
[175] Wang Z., Wang Y., and Liu Y. Global synchronization for discrete-time stochastic complex networkswith randomly occurred nonlinearities and mixed time delays. IEEE Trsactions on Neural Networks,21(1):11–25,2010.
[176] Guo L., Nian X., and Pan H. Synchronization criteria for general coupling complex networks withtime varying delay. Control Theory&Applications,28(1):73–78,2011.
[177] Fan Y.Q., Wang Y.H., Zhang Y., and Wang Q.R. The synchronization of complex dynamicalnetworks with similar nodes and coupling time-delay. Applied Mathematics and Computation,219(12):6719–6728,2013.
[178] Lee T.H., Wu Z.G., and Park J.H. Synchronization of a complex dynamical network with couplingtime-varying delays via sampled-data control. Applied Mathematics and Computation,219(3):1354–1366,2012.
[179] Wu Z.G., Park J.H., Su H.Y., Song B., and Chu J. Exponential synchronization for complex dynam-ical networks with sampled-data. Journal of the Franklin Institute,349(9):2735–2749,2012.
[180] Guan Z.H., Yang S.H., and Yao J. Stability analysis and∞control for hybrid complex dynamicalnetworks with coupling delays. International Journal of Robust and Nonlinear Control,22(2):205–222,2012.
[181] Song Q., Cao J.D., and Liu F. Pinning-controlled synchronization of hybrid-coupled complex dy-namical networks with mixed time-delays. International Journal of Robust and Nonlinear Control,22(6):690–706,2012.
[182] Li L.X., Kurths J., Peng H.P., Yang Y.X., and Luo Q. Exponentially asymptotic synchronizationof uncertain complex time-delay dynamical networks. The European Physical Journal B,86:125,2013.
[183] Ma Q., Wang Z., and Lu J.W. Finite-time synchronization for complex dynamical networks withtime-varying delays. Nonlinear Dynamics,70(1):841–848,2012.
[184] Zhou J.P., Wang Z., Wang Y.Y., and Kong Q.K. Synchronization in complex dynamical networkswith interval time-varying coupling delays. Nonlinear Dynamics,72(1-2):377–388,2013.
[185] Rao P.C., Wu Z.Y., and Liu M. Adaptive projective synchronization of dynamical networks withdistributed time delays. Nonlinear Dynamics,67(3):1729–1736,2012.
[186] Li H.J., Wong W. K., and Tang Y. Global synchronization stability for stochastic complex dynam-ical networks with probabilistic interval time-varying delays. Journal of Optimization Theory andApplications,152(2):496–516,2012.
[187] Zhou J. and Chen T. Synchronization in general complex delayed dynamical networks. IEEETransactions on Circuits and Systems I,53(3):733–744,2006.
[188] Lu J. and Ho D.W.C. Local and global synchronization in general complex dynamical networks withdelay coupling. Chaos Solitons&Fractals,37(5):1497–1510,2008.
[189] Zhu Q. and Cao J. Adaptive synchronization of chaotic cohen-crossberg neural networks with mixedtime delays. Nonlinear Dynamics,61(3):517–534,2010.
[190] Liu Y., Wang Z., Liang J., and Liu X. Synchronization and state estimation for discrete-time complexnetworks with distributed delays. IEEE Trans. Syst. Man Cybern. B, Cybern.,38(5):1314–1325,2008.
[191] Lu¨ Y., Lu¨ W., and Sun J. Convergence dynamics of stochastic reaction-diffusion recurrent neuralnetworks with continuously distributed delays. Nonlinear Anal., Real World Appl.,9:1590–1606,2008.
[192] Liu Y., Wang Z., and Liu X. Global exponential stability of generalized recurrent neural networkswith discrete and distributed delays. Neural Netw.,19(5):667–675,2006.
[193] Liu Y., Wang Z., and Liu X. Exponential synchronization of complex networks with markovianjump and mixed delays. Physics Letters A,372:3986–3998,2008.
[194] Liu Y., Wang Z., Liang J., and Liu X. Stability and synchronization of dscrete-time markovianjumping neural networks with mixed mode-dependent time delays. IEEE Trans, on Neur. netw.,20(7):1102–1117,2009.
[195] Yang G. H. and Wang J. L. Non-fragile∞control for linear systems with multiplicative controllergain variations. Automatica,37(5):727–737,2001.
[196] Park J. H. Robust non-fragile control for uncertain discrete-delay large-scale systems with a class ofcontroller gain variations. Applied Mathematics and Computation,149(1):147–164,2004.
[197] Lien C. H., Cheng W. C., Tsai C. H., and Yu K. W. Non-fragile observer-based controls for linearsystem via approach. Chaos, Solitions and Fractals,32(4):1530–1537,2007.
[198]林瑞全，杨富文.基于∞控制理论的非脆弱控制的研究.控制与决策,19(5):598–600,2004.
[199]肖伸平，吴敏，张先明.不确定时滞系统的时滞相关非脆弱鲁棒∞控制.系统科学与数学,27(3):401–411,2007.
[200] Li X. Y. and Xing W. Non-fragile passive control for uncertain singular time-delay systems. Inter-national Journal of Information and Systems Sciences,1(3-4):390–397,2005.
[201] Keel L.H. and Bhattacharyya S.P. Robust, fragile, or optimal? IEEE Trans. on Automatic Contr.,42(8):1098–1105,1997.
[202]熊军林，张庆灵.具有结构不确定的时滞系统的最优非脆弱保成本控制.控制理论与应用,22(3):503–506,2005.
[203]付兴建，童朝南.具有时滞依赖的不确定系统鲁棒∞保代价控制.中南大学学报(自然科学版),37(1):141–144,2006.
[204] Park J. H. Delay-dependent guaranteed cost stabilization criterion for neutral delay-differential sys-tems:matrix inequality approach. Computers and Mathematics with Applications,47(10-11):1507–1515,2004.
[205] Yu Li. and Gao F. Output feedback guaranteed cost control for uncertain discrete-time systems usinglinear matrix inequalities. Journal of Optimization Theory and Applications,113(3):621–634,2002.
[206]俞立.不确定离散系统的最优保性能控制.控制理论与应用,16(5):639–642,1999.
[207]陈国定，俞立，褚健.具有状态和控制滞后不确定系统的保性能控制器设计.自动化学报,28(2):314–316,2002.
[208]俞立，冯浩.不确定离散时滞系统的保性能控制.自动化学报,27(3):392–396,2001.
[209] Yu Li, Han Qinglong, and Sun Mingxuan. Optimal guaranteed cost control of linear uncertain sys-tems with input constraints. International Journal of Control, Automation, and Systems,3(3):397–402,2005.
[210] Yu Li and Chu J. An lmi approach to guaranteed cost control of linear uncertain time-delay systems.Automatica,35(6):1155–1159,1999.
[211] Boukas E. K. Guaranteed cost control of a markov jump linear uncertain systems using a time-multiplied cost function. Journal of Optimization Theory and Application,116(1):183–204,2003.
[212] Boukas E. K. Nonfragile control design for linear markovian jumping parameters systems. Journalof Optimization Theory and Application,122(2):241–255,2004.
[213]关新平，华长春，龙承念.不确定非线性系统的鲁棒耗散性与保性能控制.控制理论与应用,20(6):938–942,2003.
[214]李俊民，张果，杜彩霞.一类不确定多输入模糊双线性系统的鲁棒∞控制.控制理论与应用,26(11):1298–1302,2009.
[215] Lee T.H., Park J.H., Ji D.H., Kwon O.M., and Lee S.M. Guaranteed cost synchronization of acomplex dynamical network via dynamic feedback control. Applied Mathematics and Computation,218(11):6469–6481,2012.
[216] Li S.K., Zhang J.X., and Tang W.S. Robust∞output feedback control for uncertain complexdelayed dynamical networks. Computers&Mathematics with Applications,62(1):497–505,2011.
[217] Park J. H. Robust guaranteed cost control for uncertain linear differential systems of neural type.Appl Mathematics and Computation,140(2-3):523–535.,2003.
[218] Foda S. G. and Mahmoud M. S. Adaptive stabilization of delay differential systems with unknownuncertainty bounds. Int. J. Control,71(2):259–275,1998.
[219] Magdi S. M., El-Ke′bir B., and Abdulla I. Robust adaptive control of uncertain discrete-time state-delay systems. Computers and Mathematics with Application,55(12):2887–2902,2008.
[220]熊军林，张庆灵.结构不确定离散系统的最优非脆弱保成本控制.控制理论与应用,21(2):279–282,2004.
[221] Wang L., Dai H. Dong H., Shen Y., and Sun Y. Adaptive synchronization of weighted complexdynamical networks with coupling time-varying delays. Phys. Lett. A,372(20):3632–3639,2008.
[222]王磊，戴华平，孙优贤.时变复杂动力学网络的同步控制.控制理论与应用,25(4):603–607,2008.
[223] Magdi S. M. Resilient control of uncertain dynamical system. Berlin: Springer-Verlag,2004.
[224]陈国培，李俊民，杨莹.一类不确定脉冲混合系统的非脆弱控制器设计.西安电子科技大学学报,35(1):65–70,2008.
[225] Zhang Guo and Li Junmin. Non-fragile guaranteed cost control of discrete-time fuzzy bilinearsystem. Journal of Systems Engineering and Electronics,21(4):629–634,2010.
[226] Kun Ji and Dong Wei. Resilient control for wireless networked control systems. InternationalJournal of Control, Automation, and Systems,9(2):285–293,2011.
[227]李俊民，曹梦涛，沈思.时变复杂动态网络非脆弱同步算法.西安电子科技大学学报(自然科学版),39(5):156–164,2012.
[228] Wang Z., Liu Y., Li M., and Liu X. Stability analysis for stochastic cohen-grossberg neural networkswith mixed time delays. IEEE Transactions on Neural Networks,17(3):814–821,2006.
[229] Liu Y., Wang Z., and Liu X. Robust stability of discrete-time stochastic neural networks with time-varying delays. Neurocomputing,71:823–833,2008.
[230] Weir G., Wang Z., Lam J., Fraser K., Rao G., and Liu X. Robust filtering for stochastic geneticregulatory networks with time-varying delay. Mathematical Biosciences,220:73–80,2009.
[231] Liu Y., Wang Z., and Liu X. Robust∞filtering for discrete nonlinear stochastic systems withtime-varying delay. J. Math. Anal. Appl.,341:318–336,2008.
[232] Liang J., Wang Z., and Liu X. Exponential synchronization of stochastic delayed discrete-timecomplex networks. Nonlinear Dyn,53:153–165,2008.
[233] Li C., Chen L., and Aihara K. Stochastic synchronization of genetic oscillator networks. BMCSystems Biology,1:1–6,2007.
[234] Wang Y., Wang Z., and Liang J. Global synchronization for delayed complex networks with ran-domly occurring nonlinearities and multiple stochastic disturbances. J. Phys. A: Math. Theor.,42(13):135101,2009.
[235] Li H. and Yue D. Synchronization of markovian jumping stochastic complex networks with dis-tributed time delays and probabilistic interval discrete time-varying delays. J. Phys. A: Math. Theor.,43(10):105101,2010.
[236] Liang J., Wang Z., and Liu X. State estimation for coupled uncertain stochastic networks with mss-ing measurements and time-varying delays: The discrete-time case. IEEE Transactions on NeuralNetworks,20(5):781–794,2009.
[237] Ma L., Wang Z., Hu J., Bo Y., and Guo Z. Robust variance-constrained filtering for a class ofnonlinear stochastic systems with missing measurements. Signal Processing,90(6):2060–2071,2010.
[238] Gao H., Meng X., Chen T., and Lam J. Stabilization of networked control systems via dynamicoutput-feedback controllers. SIAM J. Control Optim,48(5):3643–3658,2010.
[239] Belykh I. V., Belykh V. N., and Hasler M. Blinking model and synchronization in small-worldnetworks with a time-varying coupling. Physica D,195(1-2):188–206,2004.
[240] Atay F. M., Biyikoglu T., and Jost J. Network synchronization: Spectral versus statistical properties.Physica D,224(1-2:5–41,2006.
[241] Yu W., Cao J., and Yuan K. Synchronization of switched system and application in communication.Phys. Lett. A,372:4438–4445,2008.
[242] Cao J., Wang Z., and Sun Y. Synchronization in an array of linearly stochastically coupled networkswith time delays. Phys. A,385(2):718–728,2007.
[243] Yang X. and Cao J. Stochastic synchronization of coupled neural networks with intermittent control.Phys. Lett. A,373:3259–3272,2009.
[244] Yu W. W., Chen G., and Cao J. D. Adaptive synchronization of uncertain coupled stochastic complexnetworks. Asian Journal of Control,13(3):418–429,2011.
[245] Yi J., Wang Y., Xiao J., and Huang Y. Exponential synchronization of complex dynamical networkswith markovian jump parameters and stochastic delays and its application to multi-agent systems.Commun. Nonlinear Sci. Numer. Simulat.,18(5):1175–1192,2013.
[246] Lee T.H., Ji D.H., Park J.H., and Jung H.Y. Decentralized guaranteed cost dynamic control forsynchronization of a complex dynamical network with randomly switching topology. Applied Math-ematics and Computation,219(3):996–1010,2012.
[247] Yang X. and Cao J. Finite-time stochastic synchronization of complex networks. Applied Mathe-matical Modelling,34:3631–3641,2010.
[248] Tang Y., Wong W. K., Fang J. A., and Miao Q. Y. Pinning impulsive synchronization of stochasticdelayed coupled networks. Chin. Phys. B,20(4):040513,2011.
[249] Tu L. Global synchronization of general delayed complex networks with stochastic disturbances.Chin. Phys. B,20(3):030504,2011.
[250] Yang Z. Q., Liu Z. X., Chen Z. Q., and Yuan Z. Z. Controlled synchronization of complex networkwith different kinds of nodes. J. Control Theory Appl,6(1):11–15,2008.
[251] Chen J. R., Jiao L. C., Wu J. S., and Wang X. H. Adaptive synchronization between two differentcomplex networks with time-varying delay coupling. Chinese Physics Letters,26(6):060505,2009.
[252] Zhang G., Zhang W., and Liu Z. R. Synchronization of coupled nonidentical dynamical systems.Chin. Phys.Lett.,27(3):030504,2010.
[253] Wu J. S., Jiao L. C., and Chen G. R. Cluster synchronization in a network of non-identical dynamicsystems. Chin. Phys. B,20(6):060503,2011.
[254] Kolmanovskii V. B. and Myskis A. D. Introduction to the Theory and Applications of FunctionalDifferential Equations. Dordrecht: Kluwer Academic Publishers,1999.
[255] Mao X. Stochastic Differential Equations and Appli-cations. Chichester: Horwood Pubishing,1997.
[256]廖晓昕.动力系统的稳定性理论和应用.北京:国防工业出版社,2000.
[257] Mandelbrot B. B. and Van Ness J. W. Fractional brownian motions, fractional noises and applica-tions. SIAM Review,10(4):422–437,1968.
[258] Oldham K.B and Spanier J. The fractional calculus: theory and applications of differentiation andintegration to arbitrary order. New York and London: Academic Press,1974.
[259]李岩.分数阶微积分及其在粘弹性材料和控制理论中的应用. PhD thesis,济南:山东大学,2008.
[260] West B.J., Bolognab M., and Grigolini P. Physics of fractal operators. NewYork: Springer,2003.
[261] Zalavsky G.M. Chao,fractional kinctics and anomalous transport. Phys.Rcp,371:461–580,2002.
[262] Chengbin M. and Yoichi H. First generation crone control. In Proceedings of the InternationalConference on Systems Engineering in the Service of Humans, volume2, pages130–135,1993.
[263] Oustaloup A. and Bluteau B. Fractional order control and its application of controller forrobust two-inertia speed control. In Proceedings of The4th International Conference on PowerElectronics and Motion Control, volume3, pages1477–1482,2004.
[264] Podlubny I. Fractional differential equations. New York: Academic Press,1999.
[265] Wu X.J., Lai D.R., and Lu H.T. Generalized synchronization of the fractional-order chaos in weight-ed complex dynamical networks with nonidentical nodes. Nonlinear Dynamics,69(1-2):667–683,2012.
[266] Wong W.K., Li H., and Leung S.Y.S. Robust synchronization of fractional-order complex dynamicalnetworks with parametric uncertainties. Commun Nonlinear Sci Numer Simulat,17:4877–4890,2012.
[267] Chen L., Chai Y., Wu R., Sun J., and Ma T. Cluster synchronization in fractional-order complexdynamical networks. Physics Letters A,376:2381–2388,2012.
[268] Chai Y., Chen L., Wu R., and Sun J. Adaptive pinning synchronization in fractional-order complexdynamical networks. Physica A,391:5746–5758,2012.
[269] Butzer P.L. and Westphal U. An Introduction to Fractional Calculus. Singapore: World Scientific,2000.
[270] Caputo M. Linear models of dissipation whose q is almost frequency independent-ii. GeophysicalJournal Royal Astronomical Society,13(5):529–539,1967.
[271] Keil F., Mackens W., and Werther J. Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties. Heidelberg:Springer-Verlag,1999.
[272]张凤荣.分数阶微分系统的稳定性分析. PhD thesis,上海:上海大学,2011.
[273] Diethelm K., Ford N.J., and Freed A.D. A predictor-corrector approach for the numerical solutionof fractional differential equations. Nonlinear Dynamics,29(1-4):3–22,2002.
[274] Matignon D. Stability results for fractional differential equations with applications to control pro-cessing. In Computational engineering in systems applications multiconference, proceeeding ofIMACS, IEEE-SMC, Lille, France, pages963–968,1996.
[275]秦昌茂，齐乃明，朱凯.分数阶系统变阶次状态空间建模及稳定理论.控制与决策,26(11):1757–1760,2011.
[276] Hu J. B., Han Y., and Zhao L. D. A novel stability theorem for fractional systems and its applying insynchronizing fractional chaotic system based on back-stepping approcach. Acta Phys Sin,58:2235–2239,2009.
[277] Li C. and Chen G. Chaos in the fractional order chen system and its control. Chaos Solitons&Fractals,22(3):549–554,2004.