基于矢量Lyapunov函数法的复杂系统的稳定性分析
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摘要
复杂关联系统在生活中无处不在,例如交通系统、管理系统、控制系统以及生态系统等。此类系统的特点是规模庞大、结构复杂且功能众多。这些复杂关联系统的控制问题实际上都可以转化成稳定性进行研究。换句话说,稳定性分析是复杂关联系统控制器设计的基础和目标,也是系统功能得以实现的关键。因此研究复杂关联系统的稳定性是十分必要的。
本论文以神经网络和自动化高速公路系统为应用背景,利用该方法进行了以下方面的研究：
(1)针对一类脉冲变时滞复杂关联大系统,建立了广义矢量Lyapunov函数法的稳定性判别方法。
(2)研究了一类脉冲混合时滞Cohen-Grossberg神经网络的稳定性。基于矢量Lyapunov函数法和数学归纳法,得到了该系统指数稳定的充分条件。基于驱动-响应概念,研究了两个具有可变时滞的脉冲混沌神经网络的全局指数同步性。在激活函数满足单调递增的假设条件下,利用矢量Lyapunov函数法和和数学归纳法,得到了确保驱动-响应系统全局指数同步的充分条件。
(3)研究了几类具有反应扩散项、脉冲干扰和随机干扰的神经网络。首先建立了一个引理,该引理用以处理扩散项；然后,基于矢量Lyapunov函数法和M矩阵理论,得到了这些系统的稳定性判据。判据中包含了反应扩散对系统的稳定性的影响,降低了以往判据的保守性。
(4)研究了一类具有Markovian跳变参数和反应扩散项的混合时滞神经网络的随机稳定性。基于矢量Lyapunov函数法和M矩阵理论,得到了平衡点随机稳定的充分条件。与基于LMI方法所得到稳定性条件相比,本文所得到的判据不但形式简单,并且不需要借助Matlab就可以直接进行验证。
(5)研究了一类具有脉冲干扰的非线性复杂关联大系统的模约束稳定性。以孤立子系统的指数稳定为基础,在假设关联函数满足全局Lipschitz条件的情况下,利用矢量Lyapunov函数法和数学归纳法,得到了确保系统模约束弦指数稳定的充分条件,并给出了指数收敛率。在此模型基础上,进一步引入了随机干扰,利用不确定性箱体理论和伊藤公式,得到了确保该系统模约束弦均方指数稳定的充分条件。
(6)研究了具有脉冲扰动和变时滞的顾前车辆纵向跟随系统的稳定性与控制。首先利用向量Lyapunov函数法和数学归纳法,得到了该系统群指数稳定的充分条件以及指数收敛率。然后,采用滑模变结构控制策略对车辆纵向跟随系统进行了控制器设计,并分析了被控系统的稳定性。最后,在假定车辆质量、空气阻力系数以及路面对车辆的阻力是不确定有界参数的前提下,利用准滑模控制策略,给出了脉冲时滞顾前车辆纵向跟随系统的控制器设计,并对被控系统的稳定性分析。
(7)研究了具有脉冲干扰和随机干扰的车辆跟随误差系统的模约束稳定性。首先基于不确定性箱体理论,利用矢量Lyapunov函数和伊藤公式,给出了随机车辆跟随系统的模约束均方指数稳定性的充分条件。进而,在此模型基础上,引入了脉冲干扰,利用数学归纳法,得到了该系统模约束指数稳定性的充分条件。最后,建立了具有脉冲干扰和随机干扰的车辆动力学方程；采用滑模变结构控制策略,对车辆纵向跟随系统进行了控制器设计,并对被控系统进行了稳定性分析。
针对本文得到的用于各类系统的稳定性判据和设计的控制器,通过数值仿真算例的形式对结论进行了检验。检验结果表明所取得的理论成果是正确且可行的。
There are lots of complex interconnected systems in real life, such as transport system, management system, control system, ecosystem and so on, which have the characteristics of large-scale, complex structures, multi-functions. The control problems of these complex interconnected systems can be transformed into the stability problems of the systems. In other words, the stability analysis is the basis and goal of the control design for complex interconnected system, and is very important for realizing the function of the system. Therefore it is necessary to study the stability of complex interconnected system.
In this dissertation, aiming at neural networks and automatic vehicle following system the following subjects are studied:
(1) The stability analysis method based on generalized vector Lyapunov function for a class of complex interconnected system with impulsive and time-varying delays is estabilished.
(2) The stability of a class of Cohen-Grossberg neural networks with impulsive and mixed delays is studied. On the assumption that activation function satisfies Lipschitz condition and amplification function is only with lower boundary, some sufficient conditions for the stability of the system are obtained by using vector Lyapunov function and mathematics induction. Besides, based on the conception of drive-response, the global exponential synchronization problem of a class of impulsive chaotic neural networks with time-varying delays is studied. Assuming that activation functions increase monotonously, by using the theory of vector Lyapunov function and mathematics induction, some sufficient conditions for the global exponential synchronization of drive system and response system are obtained.
(2) A few of neural networks with reaction-diffusion terms and impulsive and stochastic disturbance are studied. Firstly, a lemma is established to deal with the diffusion terms. Then, by using vector Lyapunov function and M matrix theory, some criteria are obtained for judging the stability of the systems. The obtained results include the influence of reaction-diffusion term on the stability of the system, and improve the conservativeness of the existing results.
(3) A class of mixed delayed neural networks with Markovian jumping parameters and reaction-diffusion terms is studied. By using vector Lyapunov function and M matrix theory, some sufficient conditions for the stochastic stability of the system are obtained. Compared to the stability based on LMI approach, the obtained results are not only with simple forms, but also can be verified directly without using Matlab.
(4) The stability with mode constraint for a class of nonlinear complex system with impulsive is studied. Based on the exponential stability of isolated subsystems, by using vector Lyapunov function and mathematics induction, some sufficient conditions for judging the stability with mode constraint of the system are obtained, and the exponential convergence rate is given. Then on this basis, stochastic disturbance is introduced into the model, by using stochastic box theory and Ito equation, some sufficient conditions for judging the exponential stability with mode constraint in the mean square are obtained.
(5) The stability and control for a class of look-ahead vehicle longitudinal following system with impulsive effects and time-varying delays are studied. Firstly, some sufficient conditions for exponential stability of the system are obtained by applying vector Lyapunov function method and mathematical induction method. Secondly, the controller for the vehicle following system is proposed by sliding mode control method, and the stability of the controlled system is analyzed based on the obtained results. Finally, assuming that the mass of vehicles, the drag coefficient and the resistance of the ground are uncertain and bounded parameters, the controller for a class of time-varying delayed look-ahead vehicle longitudinal following system with impulsive disturbance is designed based on the idea of quasi-sliding mode control, and the stability of the controlled system is analyzed by using vector Lyapunov function.
) The stability for a class of look-ahead vehicle longitudinal following system with impulsive and stochastic disturbance is studied. Firstly, by using stochastic box theory and Ito equation, some sufficient conditions for judging the exponential stability with the mode constraint in the mean square are obtained. Secondly. on this basis, the impulsive disturbance is introduced into the model. By using mathematical induction, some sufficient conditions for judging the stability with the mode constraint are obtained. Finally, the controller for the look-ahead vehicle longitudinal following system with impulsive and stochastic disturbance is designed based on the idea of sliding mode control, and the stability of the controlled system is analyzed by using vector Lyapunov function.
Aiming at the stability conditions and the designed controllers for the complex systems studied in this dissertation, some numerical examples are given to verify the obtained results. It can be concluded that the obtained theorv results are correct and feasible.
本论文以神经网络和自动化高速公路系统为应用背景,利用该方法进行了以下方面的研究：
(1)针对一类脉冲变时滞复杂关联大系统,建立了广义矢量Lyapunov函数法的稳定性判别方法。
(2)研究了一类脉冲混合时滞Cohen-Grossberg神经网络的稳定性。基于矢量Lyapunov函数法和数学归纳法,得到了该系统指数稳定的充分条件。基于驱动-响应概念,研究了两个具有可变时滞的脉冲混沌神经网络的全局指数同步性。在激活函数满足单调递增的假设条件下,利用矢量Lyapunov函数法和和数学归纳法,得到了确保驱动-响应系统全局指数同步的充分条件。
(3)研究了几类具有反应扩散项、脉冲干扰和随机干扰的神经网络。首先建立了一个引理,该引理用以处理扩散项；然后,基于矢量Lyapunov函数法和M矩阵理论,得到了这些系统的稳定性判据。判据中包含了反应扩散对系统的稳定性的影响,降低了以往判据的保守性。
(4)研究了一类具有Markovian跳变参数和反应扩散项的混合时滞神经网络的随机稳定性。基于矢量Lyapunov函数法和M矩阵理论,得到了平衡点随机稳定的充分条件。与基于LMI方法所得到稳定性条件相比,本文所得到的判据不但形式简单,并且不需要借助Matlab就可以直接进行验证。
(5)研究了一类具有脉冲干扰的非线性复杂关联大系统的模约束稳定性。以孤立子系统的指数稳定为基础,在假设关联函数满足全局Lipschitz条件的情况下,利用矢量Lyapunov函数法和数学归纳法,得到了确保系统模约束弦指数稳定的充分条件,并给出了指数收敛率。在此模型基础上,进一步引入了随机干扰,利用不确定性箱体理论和伊藤公式,得到了确保该系统模约束弦均方指数稳定的充分条件。
(6)研究了具有脉冲扰动和变时滞的顾前车辆纵向跟随系统的稳定性与控制。首先利用向量Lyapunov函数法和数学归纳法,得到了该系统群指数稳定的充分条件以及指数收敛率。然后,采用滑模变结构控制策略对车辆纵向跟随系统进行了控制器设计,并分析了被控系统的稳定性。最后,在假定车辆质量、空气阻力系数以及路面对车辆的阻力是不确定有界参数的前提下,利用准滑模控制策略,给出了脉冲时滞顾前车辆纵向跟随系统的控制器设计,并对被控系统的稳定性分析。
(7)研究了具有脉冲干扰和随机干扰的车辆跟随误差系统的模约束稳定性。首先基于不确定性箱体理论,利用矢量Lyapunov函数和伊藤公式,给出了随机车辆跟随系统的模约束均方指数稳定性的充分条件。进而,在此模型基础上,引入了脉冲干扰,利用数学归纳法,得到了该系统模约束指数稳定性的充分条件。最后,建立了具有脉冲干扰和随机干扰的车辆动力学方程；采用滑模变结构控制策略,对车辆纵向跟随系统进行了控制器设计,并对被控系统进行了稳定性分析。
针对本文得到的用于各类系统的稳定性判据和设计的控制器,通过数值仿真算例的形式对结论进行了检验。检验结果表明所取得的理论成果是正确且可行的。
There are lots of complex interconnected systems in real life, such as transport system, management system, control system, ecosystem and so on, which have the characteristics of large-scale, complex structures, multi-functions. The control problems of these complex interconnected systems can be transformed into the stability problems of the systems. In other words, the stability analysis is the basis and goal of the control design for complex interconnected system, and is very important for realizing the function of the system. Therefore it is necessary to study the stability of complex interconnected system.
In this dissertation, aiming at neural networks and automatic vehicle following system the following subjects are studied:
(1) The stability analysis method based on generalized vector Lyapunov function for a class of complex interconnected system with impulsive and time-varying delays is estabilished.
(2) The stability of a class of Cohen-Grossberg neural networks with impulsive and mixed delays is studied. On the assumption that activation function satisfies Lipschitz condition and amplification function is only with lower boundary, some sufficient conditions for the stability of the system are obtained by using vector Lyapunov function and mathematics induction. Besides, based on the conception of drive-response, the global exponential synchronization problem of a class of impulsive chaotic neural networks with time-varying delays is studied. Assuming that activation functions increase monotonously, by using the theory of vector Lyapunov function and mathematics induction, some sufficient conditions for the global exponential synchronization of drive system and response system are obtained.
(2) A few of neural networks with reaction-diffusion terms and impulsive and stochastic disturbance are studied. Firstly, a lemma is established to deal with the diffusion terms. Then, by using vector Lyapunov function and M matrix theory, some criteria are obtained for judging the stability of the systems. The obtained results include the influence of reaction-diffusion term on the stability of the system, and improve the conservativeness of the existing results.
(3) A class of mixed delayed neural networks with Markovian jumping parameters and reaction-diffusion terms is studied. By using vector Lyapunov function and M matrix theory, some sufficient conditions for the stochastic stability of the system are obtained. Compared to the stability based on LMI approach, the obtained results are not only with simple forms, but also can be verified directly without using Matlab.
(4) The stability with mode constraint for a class of nonlinear complex system with impulsive is studied. Based on the exponential stability of isolated subsystems, by using vector Lyapunov function and mathematics induction, some sufficient conditions for judging the stability with mode constraint of the system are obtained, and the exponential convergence rate is given. Then on this basis, stochastic disturbance is introduced into the model, by using stochastic box theory and Ito equation, some sufficient conditions for judging the exponential stability with mode constraint in the mean square are obtained.
(5) The stability and control for a class of look-ahead vehicle longitudinal following system with impulsive effects and time-varying delays are studied. Firstly, some sufficient conditions for exponential stability of the system are obtained by applying vector Lyapunov function method and mathematical induction method. Secondly, the controller for the vehicle following system is proposed by sliding mode control method, and the stability of the controlled system is analyzed based on the obtained results. Finally, assuming that the mass of vehicles, the drag coefficient and the resistance of the ground are uncertain and bounded parameters, the controller for a class of time-varying delayed look-ahead vehicle longitudinal following system with impulsive disturbance is designed based on the idea of quasi-sliding mode control, and the stability of the controlled system is analyzed by using vector Lyapunov function.
) The stability for a class of look-ahead vehicle longitudinal following system with impulsive and stochastic disturbance is studied. Firstly, by using stochastic box theory and Ito equation, some sufficient conditions for judging the exponential stability with the mode constraint in the mean square are obtained. Secondly. on this basis, the impulsive disturbance is introduced into the model. By using mathematical induction, some sufficient conditions for judging the stability with the mode constraint are obtained. Finally, the controller for the look-ahead vehicle longitudinal following system with impulsive and stochastic disturbance is designed based on the idea of sliding mode control, and the stability of the controlled system is analyzed by using vector Lyapunov function.
Aiming at the stability conditions and the designed controllers for the complex systems studied in this dissertation, some numerical examples are given to verify the obtained results. It can be concluded that the obtained theorv results are correct and feasible.
引文
[1]舒仲周,王照林.运动稳定性的研究进展和趋势[J].力学进展,1993,23(3)：424-431.
[2]舒仲周,张继业,曹登庆.运动稳定性[M].北京：中国铁道出版社,2001.
[3]刘斌,刘新芝,廖晓昕.不确定脉冲系统的鲁棒指数稳定性分析[J].系统工程学报,2004,19(2)：111-115.
[4]Teng, Z., On the Non-autonomous Lotka-Volterra N-species Competing Systems [J]. Applied Mathematics and Computation,2000,114(2-3):175-185.
[5]张继业.具有无穷时滞的细胞神经网络的全局稳定性分析[J].应用数学和力学,2004,25(6)：627-634.
[6]Aleksandrov, A. Y., Platonov, A. V., Aggregation and Stability Analysis of Nonlinear Complex Systems [J]. Mathematical Analysis Application,2008,342(2):989-1002.
[7]Gahinet, P., Nemirovskii, A., Laub, A., Chilali, M., LMI Control Toolbox user's Guide [M]. The Mathworks, Massachusetts,1995.
[8]Swaroop. D. and Hedrick, J. K., String Stability of Interconnected Systems [J]. IEEE Transactions on Automatic Control,1996,41(3):349-357.
[9]Zhou, J., Peng, H., Range Policy of Adaptive Cruise Control Vehicles for Improved Flow Stability and String Stability [J]. IEEE Transactions on Intelligent Transportation Systems,2005,6(2):229-237.
[10]Giuletti, F., Pollini, L., Innocenti M., Autonomous Formation Fight [J]. IEEE Control Systems Magazine,2000,20(6):34-44.
[11]Stilwell, D. J., Bishop, B. E., Platoons of Underwater Vehicles [J]. IEEE Control Systems Magazine,2000,20(6):45-52.
[12]梅凤翔,史荣昌,张永发,朱海平.约束力学系统的运动稳定性[M].北京理工大学出版社,1997.
[13]朱海平,梅凤翔.非完整系统稳定性的若干进展[J].力学进展,1998,28(1)：17-329.
[14]梅凤翔.非完整力学[J].力学进展,2001,31(1)：103-142.
[15]蒋宗礼.人工神经网络导论[M],高等教育出版社,2008.
[16]Bouzerdoum, A., Pattison, T. R., Neural Networks for Quadratic Optimization with Bound Constraints [J]. IEEE Transactions on Neural Networks,1993.4(2).293-303.
[17]Forti, M., Tesi, A.. New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems [J]. IEEE Transactions on Circuits and Systems-Ⅰ,1995,42(7):354-366.
[18]Michel, A. N., Farrell, J. A., Porod, W.. Qualitative Analysis of Neural Networks [J]. IEEE Transactions on Circuits and Systems,1989,36(2):229-243.
[19]沈国江,胡丹,孙优贤,城市高速公路交通的神经网络建模与控制[J].信息与控制.2004,33(6)：729-734.
[20]Li, Y. K. and Lu, L.H., Global Exponential Stability and Existence of Periodic Solution of Hopfield-type Neural Networks with Impulses [J]. Physics Letters A, 2004,333(1-2):62-71.
[21]Xiong, W. M., Zhou, Q., Xiao, B. and Yu, Y, Global Exponential Stability of Cellular Neural Networks with Mixed Delays and Impulses [J]. Chaos, Solitons & Fractals,2007,34(3):896-902.
[22]Ho, W. D., Liang, J. L. and Lam, J., Global Exponential Stability of Impulsive High-order BAM Neural Networks with Time-varying Delays [J]. Neural Networks, 2006,19(10):1581-1590.
[23]Bai, C. Z., Global Exponential Stability and Existence of Periodic Solution of Cohen-Grossberg Type Neural Networks with Delays and Impulses [J]. Nonlinear Analysis:Real World Applications,2008,9(2):747-761.
[24]郑伟范,张继业.具有反应扩散的神经网络的稳定性分析[J].西南交通大学学报,2004,39(1)：117-120.
[25]Allegretto, W., Panpini, D., Stability for Delayed Reaction-diffusion Neural Networks [J]. Physics Letters A,2007,360(6):669-680.
[26]楼旭阳,崔宝同.具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性[J].控制理论与应用,2008,25(4)：619-622.
[27]丛爽,王怡雯.随机神经网络发展现状综述[J].控制理论与应用,2004,21(6)：975-981.
[28]汪荣鑫.随机过程,西安交通大学出版社,2006.
[29]任殿波.自动化公路系统车辆纵横向控制[D].西南交通大学,2008.
[30]施继忠.张继业,徐晓惠.时滞随机关联系统的群稳定性[J].自动化学报,2010.36(12)：1744-1751.
[31]Hop field. J. J., Neural Networks and Physical Systems with Emergent Collective Abilities. Proceedings of the National Academy of Sciences,1982,79:2554-2558.
[32]Cohen. M. A., Grossberg, S., Absolute Stability and Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks [J]. IEEE Transactions on systems, Man and Cybernetics Society,1983,13(5):815-825.
[33]Chua, L. O., Yang, L., Cellular Neural Networks Theory [J]. IEEE Transactions on Circuits and Systems,1988,35(10):1257-1272.
[34]Kosko, B., Bidirectional Associative Memories [J]. IEEE. Transactions on Systems Man and and Cybernetics Society,1998,18 (1):49-60.
[35]Joy, M., Results Concerning the Absolute Stability of Delayed Neural Networks [J]. Neural Networks,2000,13(6):613-616.
[36]Xiong, W. J., Cao, J., Absolutely Exponential Stability of Cohen-Grossberg neural Networks with Unbounded Delays [J]. Neurocomputing 2005,68(1):1-12.
[37]Zhang, J. Y., Suda, Y., Komine H., Global Exponential Stability of Cohen-Grossberg Neural Networks with Variable Delays [J]. Physics Letters A,2005.338(1):44-50.
[38]Wang, L., Zou, X. F., Exponential Stability of Cohen-Grossberg Neural Networks [J]. Neural Networks,2002,15(3):415-422.
[39]Lu, H. T., Absolute Exponential Stability Analysis of Delayed Neural Networks [J]. Physics Letters A,2005,336(2-3):133-140.
[40]Zhang, J. Y., Suda, Y., Iwasa, T., Absolutely Exponential Stability of a Class of Neural Networks with Unbounded Delayed [J]. Neural Networks,2004,17(3): 391-397.
[41]Huang, H. and Cao, J. D., On Global Asymptotic Stability of Recurrent Neural Networks with Time-varying Delays [J]. Applied Mathematics and Computation, 2003.142(1):143-154.
[42]Liu, J., Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-varying Delays [J]. Chaos, Solitons and Fractals.2005,26(3):935-945.
[43]Joy, M., Results Concerning the Absolute Stability of Delayed Neural Networks [J]. Neural Networks,2000,13(6):613-616.
[44]Mohamad, S., Gopalsamy, K., Exponential Stability of Continuous-time and Discrete-time Cellular Neural Networks with Delays [J]. Applied Mathematics and Computation,2003,135(1):17-38.
[45]Singh, V., Some Remarks on Global Asymptotic Stability of Neural Networks with Constant Time Delay [J]. Chaos, Solitons and Fractals,2007,32(5):1720-1724.
[46]Kwon, O. M., Park, J. H., Improved Delay-dependent Stability Criterion for Neural Networks with Time-varying Delays [J]. Physics Letters A,2009,373(5):529-535.
[47]Park, J. H., On Global Stability Criterion of Neural Networks with Continuously Distributed Delays [J]. Chaos, Solitons and Fractals,2008,37(2):444-449.
[48]Cao, J. D., Li, X. L., Stability in Delayed Cohen-Grossberg Neural Networks:LMI Optimization Approach [J]. Physica D:Nonlinear Phenomena,2005,212(1-2): 54-65.
[49]Lakshmikantham, V., Bainov, D. D., Simeonov, P. S., Theory of Impulsive Differential Equations [M]. World Scientific, Singapore,1989.
[50]Gopalsamy. K., Stability of Artificial Neural Networks with Impulses [J]. Applied Mathematics and Computation,2004,154(3):783-813.
[51]Xu, D. Y., Yang, Z. C., Impulsive Delay Differential Inequality and Stability of Neural Networks [J]. Mathematical Analysis and Applications,2005,305(1): 107-120.
[52]Yang, Z. C., Xu, D. Y.. Impulsive Effects on Stability of Cohen-Grossberg Neural Networks with Variable Delays [J]. Applied Mathematics and Computation,2006, 177(1):63-78.
[53]Ahmada, S., Stamovab, I. M., Global Exponential Stability for Impulsive Cellular Neural Networks with Time-varying Delays [J]. Nonlinear Analysis:Theory, Methods & Applications,2008.69(3):786-795.
[54]王林山,徐道义.变时滞反应扩散Hopfield神经网络的全局指数稳定性[J].中国科学(E辑),2003,33(6)：488-495.
[55]Allegretto, W., Papini, D., Stability for Delayed Reaction-diffusion Neural Networks [J]. Physics Letters A,2007,360(6):669-680.
[56]Wang. L. S., Zhang. R. J., Wang, Y. F., Global Exponential Stability of Reaction-diffusion Cellular Neural Networks with S-type Distributed Time Delays [J]. Nonlinear Analysis:Real World Applications.2009.10(2):1101-1113.
[57]Li, K. L., Song, Q. K., Exponential Stability of Impulsive Cohen-Grossberg Neural Networks with Time-varying Delays and Reaction-diffusion Terms [J]. Neurocomputing,2008.72(1-3):231-240.
[58]Lu, J. G., Global Exponential Stability and Periodicity of Reaction-diffusion Delayed Recurrent Neural Networks with Dirichlet Boundary Conditions [J]. Chaos, Solitons and Fractals,2008.35(1):116-125.
[59]Li, Z., Li, K. L., Stability Analysis of Impulsive Fuzzy Cellular Neural Networks with Distributed Delays and Reaction-diffusion Terms [J]. Chaos, Solitons and Fractals.2009.42(1):492-499.
[60]Qiu, J. L., Exponential Stability of Impulsive Neural Networks with Time-varying Delays and Reaction-diffusion Terms [J]. Neurocomputing,2007,70(4-6): 1102-1108.
[61]Harkin, S. Neural Networks [M]. Prentice-Hall, NJ,1994.
[62]Wang, Z. D., Liu, Y. R., Fraser, K., Liu, X. H., Stochastic Stability of Uncertain Hopfield Neural Networks with Discrete and Distributed Delays [J]. Physics Letters A,2006,354(4):288-297.
[63]Huang, C. X., Chen, P., He, Y. G, Huang, L. H., Tan,W., Almost Sure Exponential Stability of Delayed Hopfield Neural Networks [J]. Applied Mathematics Letters, 2008,21(7):701-705.
[64]Huang, C. X., Cao, J. D., Almost Sure Exponential Stability of Stochastic Cellular Neural Networks with Unbounded Distributed Delays [J]. Neurocomputing,2009, 72(13-15):3352-3356.
[65]Lu, J. X., Ma, Y. C., Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks [J]. Chaos, Solitons and Fractals,2008, 38(5):1323-1331.
[66]Song, Q. K., Wang, Z. D., Stability Analysis of Impulsive Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays [J]. Physics Letters A, 2008,387(13):3314-3326.
[67]Tang, Y., Fang. J. A., Xia. M., Yu, D. M., Delay-distribution-dependent Stability of Stochastic Discrete-time Neural Networks with Randomly Mixed Time-varying Delays [J]. Neurocomputing.2009.72(16-18):3830-3838.
[68]Wu, Y. Y., Wu, Y. Q., Chen, Y. G., Mean Square Exponential Stability of Uncertain Stochastic Neural Networks with Time-varying Delay [J]. Neurocomputing,2009, 72(10-12):2379-2384.
[69]Huang, H., Cao. J. D., Exponential Stability Analysis of Uncertain Stochastic Neural Networks with Multiple Delays [J]. Nonlinear Analysis:RealWorld Applications, 2007,8(2):646-653.
[70]罗绮,邓其飞,包俊东,赵碧蓉,傅予力.具有分布参数的随机神经网络的镇定[J].中国科学,E辑,2004,34(6)：619-628.
[71]张子芳,徐道义,邓瑾.随机时滞反应扩散神经网络的指数稳定性[J].工程数学学报.2008,25(2)：219-223.
[72]Wan, L., Zhou, Q. H., Exponential Stability of Stochastic Reaction-diffusion Cohen-Grossberg Neural Networks with Delays [J]. Applied Mathematics and Computation,2008,206(2):818-824.
[73]Lv, Y., Lv, W., Sun. J. H., Convergence Dynamics of Stochastic Reaction-diffusion Recurrent Neural Networks with Continuously Distributed Delays [J]. Nonlinear Analysis:Real World Applications,2008,9(4):1590-1606.
[74]Zhou, Q., Wan, L., Exponential Stability of Stochastic Delayed Hopfield Neural Networks [J]. Applied Mathematics and Computation,2008,199(1):84-89.
[75]Zhu, Q. X. and Cao, J. D., Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays [J]. IEEE Transaction on Neural Networks,2010,21(8):1314-1325.
[76]Lou, X. Y., Cui B. T., Stochastic Stability Analysis for Delayed Neural Networks of Neutral Type with Markovian Jump Parameters [J]. Chaos, Solitons and Fractals 2009; 39(5):2188-2197.
[77]王顺康,王林山.具有马尔可夫跳跃参数的变时滞静态神经网络的全局指数稳定性[J].山东大学学报,2008.43(4)：81-84.
[78]Lou, X. Y., Cui, B. T., Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks with Time-varying Delays [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics,2007,37(3):713-719.
[79]Wang, Z. D., Liu, Y. R., Yu, L., Liu, X. H., Exponential Stability of Delayed Recurrent Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2006,356(4-5):346-352.
[80]Wang, G. J., Cao, J. D., Xu. M., Stability Analysis for Stochastic BAM Neural Networks with Markovian Jumping Parameters [J]. Neurocomputing,2009, 72(16-18):3901-3906.
[81]Han, W., Liu, Y., Wang, L. S., Robust Exponential Stability of Markovian Jumping Neural Networks with Mode-dependent Delay [J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(9):2529-2535.
[82]Li, H. Y., Chen, B., Zhou, Q., Lin, C., Robust Exponential Stability for Delayed Uncertain Hopfield Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2008,372(30):4996-5003.
[83]Wang, L. S., Zhang, Z., Wang, Y. F., Stochastic Exponential Stability of the Delayed Reaction-diffusion Recurrent Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2008,372(18):3201-3209.
[84]Balasubramaniam, P.. Vidhya, C. Global Asymptotic Stability of Stochastic BAM Neural Networks with Distributed Delays and Reaction-diffusion Terms [J]. Computational and Applied Mathematics.2010,234(12):3458-3466.
[85]Balasubramaniam, P., Vidhya, C., Exponential Stability of Stochastic Reaction-diffusion Uncertain Fuzzy Neural Networks with Mixed Delays and Markovian Jumping Parameters [J]. Expert Systems with Applications,2012,39(3): 3109-3115.
[86]Gao, J. G., Deng, F. Q., Zhang, C. K., Sun,Y. F., Asymptotic Stability of Stochastic Impulsive System via Comparison Approach (C).2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics, pp.181-184.
[87]Yao, F. Q., Deng, F. Q., Comparison Principle and Stability of Impulsive Stochastic Functional Differential Systems in Terms of Two Measures [C].2010 8th IEEE International Conference on Control and Automation, Xiamen, China, June 9-11, 2010, pp.333-338.
[88]Liu. B., Stability of Solutions for Stochastic Impulsive Systems via Comparison Approach [J]. IEEE Transactions on Automatic Control,2008,53(9):2128-2033.
[89]Li, C. X., Sun, J. T., Sun, R. Y., Stability Analysis of a Class of Stochastic Differential Delay Equations with Nonlinear Impulsive Effects [J]. Journal of the Franklin Institute,2010,347(7):1186-1198.
[90]Yang, J., Zhong, S. M., Luo. W. P., Mean Square Stability Analysis of Impulsive Stochastic Differential Equations with Delays [J]. Computational and Applied Mathematics,2008,216(2):474-483.
[91]Pan, L. J., Cao, J. D., Exponential Stability of Impulsive Stochastic Functional Differential Equations [J]. Mathematical Analysis and Applications,2011,382(2): 672-685.
[92]Yang. Z. G., Xu, D. Y. Xiang L., Exponential P-stability of Impulsive Stochastic Differential Equations with Delays [J]. Physics Letters A.2006,359(2):129-137.
[93]Chu, K. C., Decentralized Control of High-speed Vehicle Strings [J]. Transportation Research:Part B.1974,8(3):362-383.
[94]Barbieri, E.. Stability Analysis of a Class of Interconnected Systems [J]. ASME Journal of Dynamic System, Measurements, Control,1993,115(3):546-551.
[95]Swaroop. D. and Hedrick, J. K., String Stability of Interconnected Systems [J]. IEEE Transaction Automatic Control.1996,41(3):349-357.
[96]Swaroop, D. and Hedrick, J. K., Constant Spacing Strategies for Platooning in Automated Highway Systems [J]. ASME Journal of Dynamic Systems, Measurement and Control,1999,121:462-470.
[97]Zhang. J. Y., Suda. Y. Iwasa. T. et al. Vector Lyapunov Function Approach to Longitudinal Control of Vehicles in a Platoon [J]. JSME International Journal (Series C).2004.47(2):653-658.
[98]任殿波,张继业,孙林夫.基于向量Liapunov函数方法的时滞车辆跟随系统稳定性分析[J].交通运输工程学报,2007,7(4)：89-92.
[99]任殿波,张继业.基于Lyapunov函数方法的时滞车辆纵向跟随控制[J].控制与决策,2007,22(8)：921-944.
[100]Socha, L. Stochastic Stability of Interconnected String Systems [J]. Chaos, Solitons and Fractals,2004,19(4):949-955.
[101]Shladover, S. E., Longitudinal Control of Automotive Vehicles in Close-formation Platoons [J]. Transportation Research,1980,14(2):63-81.
[102]Fujioka, T., Longitudinal Vehicle Following Control Forautonomous Driving (C). Proc AVEC'96 Int Symp Advanced Vehicle Control. Aachen,1996:1293-1304.
[103]任殿波,张京明,张继业.具有不确定参数的车辆跟随滑模控制[J].电机与控制学报,2010,14(1),73-77.
[104]Aracil, J., Heredia, G. Ollero, A.. Global Stability Analysis of Fuzzy Path Tracking Using f Requency Response [J]. Engineering Applications of Artificial Intelligence, 2000,13(1):109-119.
[105]Lee, G. D., Kim, S. W., A Longitudinal Control System for a Platoon of Vehicles Using a Fuzzy-sliding Mode Algorithm [J]. Methatronics,2002,12(1):97-118.
[106]Zhou, J., Lu, J.B., and Peng, H., Vehicle Stabilization in Response to Exogenous Impulsive Disturbances to the Vehicle Body (C).2009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA, June 10-12,2009. pp.701-706.
[107]Pant, A., Seiler, P., Hedrick, K., Mesh Stability of Look-ahead, Interconnected Systems [J]. IEEE Transaction Automatic Control,2002.47(2):403-407.
[108]Pant, A., Mesh Stability of Formation of Unmanned Aerial Vehicles [D]. PhD thesis, University of Califoria, Berkeley,2002.
[109]Zhang, J. Y., Comment on "Mesh Stability of Look-Ahead Interconnected Systems'' [J]. IEEE Transactions on Automatic Control,2004,49(5):858-859.
[110]韩崇昭,王月娟,万百五.随机系统理论[M].西安交通大学出版社,1987.
[111]廖晓听,傅予力,高健等.具有反应扩散的Hopfield神经网络的稳定性[J].电子学报,2000,28(1)：78-80.
[112]Liang, J., Cao, J. C. Global Exponential Stability of Reaction-diffusion Recurrent Neural Networks with Time-varying Delays [J]. Physics Letters A,2003,314(5-6): 434-442.
[113]Song, Q. K., Zhang J. Y., Global Exponential Stability of Impulsive Cohen-Grossberg Neural Network with Time-varying Delays [J]. Nonlinear Analysis: Real World Applications,2008,9(2):500-510.
[114]Li, K., Lai, C. H., Adaptive-impulsive Synchronization of Uncertain Complex Dynamical Networks [J]. Physics Letters A,2008,372(10):1601-1606.
[115]Sun, Y. H., Cao J. D., Adaptive Lag Synchronization of Unknown Chaotic Delayed Neural Networks with Noise Perturbation [J]. Physical Letter A,2007,364(3-4): 277-285.
[116]Sun, J. T., Delay-dependent Stability Criteria for Time-delay Chaotic Systems Via Time-delay Feedback Control [J]. Chaos, Solitons & Fractals,2004,21(1):143-150.
[117]Lin, J., Zhang, J. Y., Global Exponential Synchronization of a Class of Chaotic Neural Networks with Time-varying Delays [J]. Lecture notes in computer science, 2007,4682(1):75-82.
[118]Li, B., Xu. D. Y., Mean Square Asymptotic Behavior of Stochastic Neural Networks with Infinitely Distributed Delays [J]. Neurocomputing,2009,72(13-15): 3311-3317.
[119]Sathy, R., Balasubramaniam, P., Stability Analysis of Fuzzy Markovian Jumping Cohen-Grossberg BAM Neural Networks with Mixed Time-varying Delays [J]. Communications in Nonlinear Science and Numerical Simulation,2011,16(4): 2054-2064.
[120]Lou, X. Y., Cui, B. T., Stochastic Stability Analysis for Delayed Neural Networks of Neutral Type with Markovian Jump Parameters [J]. Chaos, Solitons and Fractals, 2009.39(5):2188-2197.
[121]Lou, X. Y., Cui, B. T., Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks with Time-varying Delays [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics,2007,37(3):713-719.
[122]Liu. H. Y., Zhao, L. Zhang, Z. X., Ou Y. Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays. Neurocomputing 2009:72(16-18):3669-3676.
[123]Wang, G. J., Cao, J. D., Xu, M., Stability Analysis for Stochastic BAM Neural Networks with Markovian Jumping Parameters [J], Neurocomputing,2009, 72(16-18):3901-3906.
[124]Han. W., Liu,Y., Wang, L.S., Robust Exponential Stability of Markovian Jumping Neural Networks with Mode-dependent Delay[J]. Communications in Nonlinear Science and Numerical Simulation.2010,15(9):2529-2535.
[125]Li, H.Y., Chen. B., Zhou, Q. Lin, C., Robust Exponential Stability for Delayed Uncertain Hopfield Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2008,372(30):4996-5003.
[126]Ei-Sayed, M. L., Krishnaprasad, P. S., Homogenous Interconnected Systems:A Example [J]. IEEE Transaction Automatic Control,1981,26(4):894-901.
[127]Davison, E. J., Tripathi, N., The Optimal Decentralized Control of a Large Power System:Load and Frequence control [J]. IEEE Transaction Automatic Control,1978, 23(2):312-325.
[128]Barbieri, E., Stability Analysis of a Class of Interconnected Systems [J]. ASME Journal of Dynamic System, Measurements, Control,1993,115(3):546-551.
[129]Siljak, D. D., Large-scale Dynamic Systems Stability and Structure [M]. North-Holland:Amstrerdam,1978.
[130]文海霞.一类时滞非线性动力系统的全局指数稳定性[J].科学技术与工程,2009.9(2)：430-433.
[131]张继业,杨翊仁,曾京.无限维关联系统的弦稳定性[J].应用数学和力学,2000,21(7)：715-719.
[132]Liu, B., Teo, K. L., Liu, X. Z., Robust Exponential Stabilization for Large-scale Uncertain Impulsive Systems with Coupling Time-delays [J]. Nonlinear Analysis. 2008,68(5):1169-1183.
[133]Pant, A., Mesh Stability of Look-ahead Interconnected Systems [J]. IEEE Transaction on Automatic Control,2003,47(2):403-408.
[134]Khasminski, R. Z., Stochastic Stability of Differential Equations [M]. Groningen. The Netherlands:Sijthoff & Noordhoff,1980.
[135]Slotine, J. E., Li, W. P.,应用非线性控制[M].北京：机械工业出版社,2004.
[136]任殿波,张策,张继业.考虑前后信息的车辆跟随自适应控制[J].哈尔滨工业大学学报.2011,43(6)：76-80.
[137]任殿波,张京明,张继业.具有不确定参数的车辆跟随滑模控制[J].电机与控制学报.2010,14(1)：73-77.
[138]Niu,Y. G., Ho, W.C. D., Robust Observer Design for Ito Stochastic Time-delay Systems via Sliding Mode Control [J]. Systems & Control Letters,2006,55(10): 781-793.
[139]Higham, D. J., An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations [J]. Society for Industrial and Applied Mathematics.2001, 43(3):525-546.
[2]舒仲周,张继业,曹登庆.运动稳定性[M].北京：中国铁道出版社,2001.
[3]刘斌,刘新芝,廖晓昕.不确定脉冲系统的鲁棒指数稳定性分析[J].系统工程学报,2004,19(2)：111-115.
[4]Teng, Z., On the Non-autonomous Lotka-Volterra N-species Competing Systems [J]. Applied Mathematics and Computation,2000,114(2-3):175-185.
[5]张继业.具有无穷时滞的细胞神经网络的全局稳定性分析[J].应用数学和力学,2004,25(6)：627-634.
[6]Aleksandrov, A. Y., Platonov, A. V., Aggregation and Stability Analysis of Nonlinear Complex Systems [J]. Mathematical Analysis Application,2008,342(2):989-1002.
[7]Gahinet, P., Nemirovskii, A., Laub, A., Chilali, M., LMI Control Toolbox user's Guide [M]. The Mathworks, Massachusetts,1995.
[8]Swaroop. D. and Hedrick, J. K., String Stability of Interconnected Systems [J]. IEEE Transactions on Automatic Control,1996,41(3):349-357.
[9]Zhou, J., Peng, H., Range Policy of Adaptive Cruise Control Vehicles for Improved Flow Stability and String Stability [J]. IEEE Transactions on Intelligent Transportation Systems,2005,6(2):229-237.
[10]Giuletti, F., Pollini, L., Innocenti M., Autonomous Formation Fight [J]. IEEE Control Systems Magazine,2000,20(6):34-44.
[11]Stilwell, D. J., Bishop, B. E., Platoons of Underwater Vehicles [J]. IEEE Control Systems Magazine,2000,20(6):45-52.
[12]梅凤翔,史荣昌,张永发,朱海平.约束力学系统的运动稳定性[M].北京理工大学出版社,1997.
[13]朱海平,梅凤翔.非完整系统稳定性的若干进展[J].力学进展,1998,28(1)：17-329.
[14]梅凤翔.非完整力学[J].力学进展,2001,31(1)：103-142.
[15]蒋宗礼.人工神经网络导论[M],高等教育出版社,2008.
[16]Bouzerdoum, A., Pattison, T. R., Neural Networks for Quadratic Optimization with Bound Constraints [J]. IEEE Transactions on Neural Networks,1993.4(2).293-303.
[17]Forti, M., Tesi, A.. New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems [J]. IEEE Transactions on Circuits and Systems-Ⅰ,1995,42(7):354-366.
[18]Michel, A. N., Farrell, J. A., Porod, W.. Qualitative Analysis of Neural Networks [J]. IEEE Transactions on Circuits and Systems,1989,36(2):229-243.
[19]沈国江,胡丹,孙优贤,城市高速公路交通的神经网络建模与控制[J].信息与控制.2004,33(6)：729-734.
[20]Li, Y. K. and Lu, L.H., Global Exponential Stability and Existence of Periodic Solution of Hopfield-type Neural Networks with Impulses [J]. Physics Letters A, 2004,333(1-2):62-71.
[21]Xiong, W. M., Zhou, Q., Xiao, B. and Yu, Y, Global Exponential Stability of Cellular Neural Networks with Mixed Delays and Impulses [J]. Chaos, Solitons & Fractals,2007,34(3):896-902.
[22]Ho, W. D., Liang, J. L. and Lam, J., Global Exponential Stability of Impulsive High-order BAM Neural Networks with Time-varying Delays [J]. Neural Networks, 2006,19(10):1581-1590.
[23]Bai, C. Z., Global Exponential Stability and Existence of Periodic Solution of Cohen-Grossberg Type Neural Networks with Delays and Impulses [J]. Nonlinear Analysis:Real World Applications,2008,9(2):747-761.
[24]郑伟范,张继业.具有反应扩散的神经网络的稳定性分析[J].西南交通大学学报,2004,39(1)：117-120.
[25]Allegretto, W., Panpini, D., Stability for Delayed Reaction-diffusion Neural Networks [J]. Physics Letters A,2007,360(6):669-680.
[26]楼旭阳,崔宝同.具反应扩散混合时滞Cohen-Grossberg神经网络的指数耗散性[J].控制理论与应用,2008,25(4)：619-622.
[27]丛爽,王怡雯.随机神经网络发展现状综述[J].控制理论与应用,2004,21(6)：975-981.
[28]汪荣鑫.随机过程,西安交通大学出版社,2006.
[29]任殿波.自动化公路系统车辆纵横向控制[D].西南交通大学,2008.
[30]施继忠.张继业,徐晓惠.时滞随机关联系统的群稳定性[J].自动化学报,2010.36(12)：1744-1751.
[31]Hop field. J. J., Neural Networks and Physical Systems with Emergent Collective Abilities. Proceedings of the National Academy of Sciences,1982,79:2554-2558.
[32]Cohen. M. A., Grossberg, S., Absolute Stability and Global Pattern Formation and Parallel Memory Storage by Competitive Neural Networks [J]. IEEE Transactions on systems, Man and Cybernetics Society,1983,13(5):815-825.
[33]Chua, L. O., Yang, L., Cellular Neural Networks Theory [J]. IEEE Transactions on Circuits and Systems,1988,35(10):1257-1272.
[34]Kosko, B., Bidirectional Associative Memories [J]. IEEE. Transactions on Systems Man and and Cybernetics Society,1998,18 (1):49-60.
[35]Joy, M., Results Concerning the Absolute Stability of Delayed Neural Networks [J]. Neural Networks,2000,13(6):613-616.
[36]Xiong, W. J., Cao, J., Absolutely Exponential Stability of Cohen-Grossberg neural Networks with Unbounded Delays [J]. Neurocomputing 2005,68(1):1-12.
[37]Zhang, J. Y., Suda, Y., Komine H., Global Exponential Stability of Cohen-Grossberg Neural Networks with Variable Delays [J]. Physics Letters A,2005.338(1):44-50.
[38]Wang, L., Zou, X. F., Exponential Stability of Cohen-Grossberg Neural Networks [J]. Neural Networks,2002,15(3):415-422.
[39]Lu, H. T., Absolute Exponential Stability Analysis of Delayed Neural Networks [J]. Physics Letters A,2005,336(2-3):133-140.
[40]Zhang, J. Y., Suda, Y., Iwasa, T., Absolutely Exponential Stability of a Class of Neural Networks with Unbounded Delayed [J]. Neural Networks,2004,17(3): 391-397.
[41]Huang, H. and Cao, J. D., On Global Asymptotic Stability of Recurrent Neural Networks with Time-varying Delays [J]. Applied Mathematics and Computation, 2003.142(1):143-154.
[42]Liu, J., Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-varying Delays [J]. Chaos, Solitons and Fractals.2005,26(3):935-945.
[43]Joy, M., Results Concerning the Absolute Stability of Delayed Neural Networks [J]. Neural Networks,2000,13(6):613-616.
[44]Mohamad, S., Gopalsamy, K., Exponential Stability of Continuous-time and Discrete-time Cellular Neural Networks with Delays [J]. Applied Mathematics and Computation,2003,135(1):17-38.
[45]Singh, V., Some Remarks on Global Asymptotic Stability of Neural Networks with Constant Time Delay [J]. Chaos, Solitons and Fractals,2007,32(5):1720-1724.
[46]Kwon, O. M., Park, J. H., Improved Delay-dependent Stability Criterion for Neural Networks with Time-varying Delays [J]. Physics Letters A,2009,373(5):529-535.
[47]Park, J. H., On Global Stability Criterion of Neural Networks with Continuously Distributed Delays [J]. Chaos, Solitons and Fractals,2008,37(2):444-449.
[48]Cao, J. D., Li, X. L., Stability in Delayed Cohen-Grossberg Neural Networks:LMI Optimization Approach [J]. Physica D:Nonlinear Phenomena,2005,212(1-2): 54-65.
[49]Lakshmikantham, V., Bainov, D. D., Simeonov, P. S., Theory of Impulsive Differential Equations [M]. World Scientific, Singapore,1989.
[50]Gopalsamy. K., Stability of Artificial Neural Networks with Impulses [J]. Applied Mathematics and Computation,2004,154(3):783-813.
[51]Xu, D. Y., Yang, Z. C., Impulsive Delay Differential Inequality and Stability of Neural Networks [J]. Mathematical Analysis and Applications,2005,305(1): 107-120.
[52]Yang, Z. C., Xu, D. Y.. Impulsive Effects on Stability of Cohen-Grossberg Neural Networks with Variable Delays [J]. Applied Mathematics and Computation,2006, 177(1):63-78.
[53]Ahmada, S., Stamovab, I. M., Global Exponential Stability for Impulsive Cellular Neural Networks with Time-varying Delays [J]. Nonlinear Analysis:Theory, Methods & Applications,2008.69(3):786-795.
[54]王林山,徐道义.变时滞反应扩散Hopfield神经网络的全局指数稳定性[J].中国科学(E辑),2003,33(6)：488-495.
[55]Allegretto, W., Papini, D., Stability for Delayed Reaction-diffusion Neural Networks [J]. Physics Letters A,2007,360(6):669-680.
[56]Wang. L. S., Zhang. R. J., Wang, Y. F., Global Exponential Stability of Reaction-diffusion Cellular Neural Networks with S-type Distributed Time Delays [J]. Nonlinear Analysis:Real World Applications.2009.10(2):1101-1113.
[57]Li, K. L., Song, Q. K., Exponential Stability of Impulsive Cohen-Grossberg Neural Networks with Time-varying Delays and Reaction-diffusion Terms [J]. Neurocomputing,2008.72(1-3):231-240.
[58]Lu, J. G., Global Exponential Stability and Periodicity of Reaction-diffusion Delayed Recurrent Neural Networks with Dirichlet Boundary Conditions [J]. Chaos, Solitons and Fractals,2008.35(1):116-125.
[59]Li, Z., Li, K. L., Stability Analysis of Impulsive Fuzzy Cellular Neural Networks with Distributed Delays and Reaction-diffusion Terms [J]. Chaos, Solitons and Fractals.2009.42(1):492-499.
[60]Qiu, J. L., Exponential Stability of Impulsive Neural Networks with Time-varying Delays and Reaction-diffusion Terms [J]. Neurocomputing,2007,70(4-6): 1102-1108.
[61]Harkin, S. Neural Networks [M]. Prentice-Hall, NJ,1994.
[62]Wang, Z. D., Liu, Y. R., Fraser, K., Liu, X. H., Stochastic Stability of Uncertain Hopfield Neural Networks with Discrete and Distributed Delays [J]. Physics Letters A,2006,354(4):288-297.
[63]Huang, C. X., Chen, P., He, Y. G, Huang, L. H., Tan,W., Almost Sure Exponential Stability of Delayed Hopfield Neural Networks [J]. Applied Mathematics Letters, 2008,21(7):701-705.
[64]Huang, C. X., Cao, J. D., Almost Sure Exponential Stability of Stochastic Cellular Neural Networks with Unbounded Distributed Delays [J]. Neurocomputing,2009, 72(13-15):3352-3356.
[65]Lu, J. X., Ma, Y. C., Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks [J]. Chaos, Solitons and Fractals,2008, 38(5):1323-1331.
[66]Song, Q. K., Wang, Z. D., Stability Analysis of Impulsive Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays [J]. Physics Letters A, 2008,387(13):3314-3326.
[67]Tang, Y., Fang. J. A., Xia. M., Yu, D. M., Delay-distribution-dependent Stability of Stochastic Discrete-time Neural Networks with Randomly Mixed Time-varying Delays [J]. Neurocomputing.2009.72(16-18):3830-3838.
[68]Wu, Y. Y., Wu, Y. Q., Chen, Y. G., Mean Square Exponential Stability of Uncertain Stochastic Neural Networks with Time-varying Delay [J]. Neurocomputing,2009, 72(10-12):2379-2384.
[69]Huang, H., Cao. J. D., Exponential Stability Analysis of Uncertain Stochastic Neural Networks with Multiple Delays [J]. Nonlinear Analysis:RealWorld Applications, 2007,8(2):646-653.
[70]罗绮,邓其飞,包俊东,赵碧蓉,傅予力.具有分布参数的随机神经网络的镇定[J].中国科学,E辑,2004,34(6)：619-628.
[71]张子芳,徐道义,邓瑾.随机时滞反应扩散神经网络的指数稳定性[J].工程数学学报.2008,25(2)：219-223.
[72]Wan, L., Zhou, Q. H., Exponential Stability of Stochastic Reaction-diffusion Cohen-Grossberg Neural Networks with Delays [J]. Applied Mathematics and Computation,2008,206(2):818-824.
[73]Lv, Y., Lv, W., Sun. J. H., Convergence Dynamics of Stochastic Reaction-diffusion Recurrent Neural Networks with Continuously Distributed Delays [J]. Nonlinear Analysis:Real World Applications,2008,9(4):1590-1606.
[74]Zhou, Q., Wan, L., Exponential Stability of Stochastic Delayed Hopfield Neural Networks [J]. Applied Mathematics and Computation,2008,199(1):84-89.
[75]Zhu, Q. X. and Cao, J. D., Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks with Mixed Time Delays [J]. IEEE Transaction on Neural Networks,2010,21(8):1314-1325.
[76]Lou, X. Y., Cui B. T., Stochastic Stability Analysis for Delayed Neural Networks of Neutral Type with Markovian Jump Parameters [J]. Chaos, Solitons and Fractals 2009; 39(5):2188-2197.
[77]王顺康,王林山.具有马尔可夫跳跃参数的变时滞静态神经网络的全局指数稳定性[J].山东大学学报,2008.43(4)：81-84.
[78]Lou, X. Y., Cui, B. T., Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks with Time-varying Delays [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics,2007,37(3):713-719.
[79]Wang, Z. D., Liu, Y. R., Yu, L., Liu, X. H., Exponential Stability of Delayed Recurrent Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2006,356(4-5):346-352.
[80]Wang, G. J., Cao, J. D., Xu. M., Stability Analysis for Stochastic BAM Neural Networks with Markovian Jumping Parameters [J]. Neurocomputing,2009, 72(16-18):3901-3906.
[81]Han, W., Liu, Y., Wang, L. S., Robust Exponential Stability of Markovian Jumping Neural Networks with Mode-dependent Delay [J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(9):2529-2535.
[82]Li, H. Y., Chen, B., Zhou, Q., Lin, C., Robust Exponential Stability for Delayed Uncertain Hopfield Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2008,372(30):4996-5003.
[83]Wang, L. S., Zhang, Z., Wang, Y. F., Stochastic Exponential Stability of the Delayed Reaction-diffusion Recurrent Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2008,372(18):3201-3209.
[84]Balasubramaniam, P.. Vidhya, C. Global Asymptotic Stability of Stochastic BAM Neural Networks with Distributed Delays and Reaction-diffusion Terms [J]. Computational and Applied Mathematics.2010,234(12):3458-3466.
[85]Balasubramaniam, P., Vidhya, C., Exponential Stability of Stochastic Reaction-diffusion Uncertain Fuzzy Neural Networks with Mixed Delays and Markovian Jumping Parameters [J]. Expert Systems with Applications,2012,39(3): 3109-3115.
[86]Gao, J. G., Deng, F. Q., Zhang, C. K., Sun,Y. F., Asymptotic Stability of Stochastic Impulsive System via Comparison Approach (C).2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics, pp.181-184.
[87]Yao, F. Q., Deng, F. Q., Comparison Principle and Stability of Impulsive Stochastic Functional Differential Systems in Terms of Two Measures [C].2010 8th IEEE International Conference on Control and Automation, Xiamen, China, June 9-11, 2010, pp.333-338.
[88]Liu. B., Stability of Solutions for Stochastic Impulsive Systems via Comparison Approach [J]. IEEE Transactions on Automatic Control,2008,53(9):2128-2033.
[89]Li, C. X., Sun, J. T., Sun, R. Y., Stability Analysis of a Class of Stochastic Differential Delay Equations with Nonlinear Impulsive Effects [J]. Journal of the Franklin Institute,2010,347(7):1186-1198.
[90]Yang, J., Zhong, S. M., Luo. W. P., Mean Square Stability Analysis of Impulsive Stochastic Differential Equations with Delays [J]. Computational and Applied Mathematics,2008,216(2):474-483.
[91]Pan, L. J., Cao, J. D., Exponential Stability of Impulsive Stochastic Functional Differential Equations [J]. Mathematical Analysis and Applications,2011,382(2): 672-685.
[92]Yang. Z. G., Xu, D. Y. Xiang L., Exponential P-stability of Impulsive Stochastic Differential Equations with Delays [J]. Physics Letters A.2006,359(2):129-137.
[93]Chu, K. C., Decentralized Control of High-speed Vehicle Strings [J]. Transportation Research:Part B.1974,8(3):362-383.
[94]Barbieri, E.. Stability Analysis of a Class of Interconnected Systems [J]. ASME Journal of Dynamic System, Measurements, Control,1993,115(3):546-551.
[95]Swaroop. D. and Hedrick, J. K., String Stability of Interconnected Systems [J]. IEEE Transaction Automatic Control.1996,41(3):349-357.
[96]Swaroop, D. and Hedrick, J. K., Constant Spacing Strategies for Platooning in Automated Highway Systems [J]. ASME Journal of Dynamic Systems, Measurement and Control,1999,121:462-470.
[97]Zhang. J. Y., Suda. Y. Iwasa. T. et al. Vector Lyapunov Function Approach to Longitudinal Control of Vehicles in a Platoon [J]. JSME International Journal (Series C).2004.47(2):653-658.
[98]任殿波,张继业,孙林夫.基于向量Liapunov函数方法的时滞车辆跟随系统稳定性分析[J].交通运输工程学报,2007,7(4)：89-92.
[99]任殿波,张继业.基于Lyapunov函数方法的时滞车辆纵向跟随控制[J].控制与决策,2007,22(8)：921-944.
[100]Socha, L. Stochastic Stability of Interconnected String Systems [J]. Chaos, Solitons and Fractals,2004,19(4):949-955.
[101]Shladover, S. E., Longitudinal Control of Automotive Vehicles in Close-formation Platoons [J]. Transportation Research,1980,14(2):63-81.
[102]Fujioka, T., Longitudinal Vehicle Following Control Forautonomous Driving (C). Proc AVEC'96 Int Symp Advanced Vehicle Control. Aachen,1996:1293-1304.
[103]任殿波,张京明,张继业.具有不确定参数的车辆跟随滑模控制[J].电机与控制学报,2010,14(1),73-77.
[104]Aracil, J., Heredia, G. Ollero, A.. Global Stability Analysis of Fuzzy Path Tracking Using f Requency Response [J]. Engineering Applications of Artificial Intelligence, 2000,13(1):109-119.
[105]Lee, G. D., Kim, S. W., A Longitudinal Control System for a Platoon of Vehicles Using a Fuzzy-sliding Mode Algorithm [J]. Methatronics,2002,12(1):97-118.
[106]Zhou, J., Lu, J.B., and Peng, H., Vehicle Stabilization in Response to Exogenous Impulsive Disturbances to the Vehicle Body (C).2009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA, June 10-12,2009. pp.701-706.
[107]Pant, A., Seiler, P., Hedrick, K., Mesh Stability of Look-ahead, Interconnected Systems [J]. IEEE Transaction Automatic Control,2002.47(2):403-407.
[108]Pant, A., Mesh Stability of Formation of Unmanned Aerial Vehicles [D]. PhD thesis, University of Califoria, Berkeley,2002.
[109]Zhang, J. Y., Comment on "Mesh Stability of Look-Ahead Interconnected Systems'' [J]. IEEE Transactions on Automatic Control,2004,49(5):858-859.
[110]韩崇昭,王月娟,万百五.随机系统理论[M].西安交通大学出版社,1987.
[111]廖晓听,傅予力,高健等.具有反应扩散的Hopfield神经网络的稳定性[J].电子学报,2000,28(1)：78-80.
[112]Liang, J., Cao, J. C. Global Exponential Stability of Reaction-diffusion Recurrent Neural Networks with Time-varying Delays [J]. Physics Letters A,2003,314(5-6): 434-442.
[113]Song, Q. K., Zhang J. Y., Global Exponential Stability of Impulsive Cohen-Grossberg Neural Network with Time-varying Delays [J]. Nonlinear Analysis: Real World Applications,2008,9(2):500-510.
[114]Li, K., Lai, C. H., Adaptive-impulsive Synchronization of Uncertain Complex Dynamical Networks [J]. Physics Letters A,2008,372(10):1601-1606.
[115]Sun, Y. H., Cao J. D., Adaptive Lag Synchronization of Unknown Chaotic Delayed Neural Networks with Noise Perturbation [J]. Physical Letter A,2007,364(3-4): 277-285.
[116]Sun, J. T., Delay-dependent Stability Criteria for Time-delay Chaotic Systems Via Time-delay Feedback Control [J]. Chaos, Solitons & Fractals,2004,21(1):143-150.
[117]Lin, J., Zhang, J. Y., Global Exponential Synchronization of a Class of Chaotic Neural Networks with Time-varying Delays [J]. Lecture notes in computer science, 2007,4682(1):75-82.
[118]Li, B., Xu. D. Y., Mean Square Asymptotic Behavior of Stochastic Neural Networks with Infinitely Distributed Delays [J]. Neurocomputing,2009,72(13-15): 3311-3317.
[119]Sathy, R., Balasubramaniam, P., Stability Analysis of Fuzzy Markovian Jumping Cohen-Grossberg BAM Neural Networks with Mixed Time-varying Delays [J]. Communications in Nonlinear Science and Numerical Simulation,2011,16(4): 2054-2064.
[120]Lou, X. Y., Cui, B. T., Stochastic Stability Analysis for Delayed Neural Networks of Neutral Type with Markovian Jump Parameters [J]. Chaos, Solitons and Fractals, 2009.39(5):2188-2197.
[121]Lou, X. Y., Cui, B. T., Stochastic Exponential Stability for Markovian Jumping BAM Neural Networks with Time-varying Delays [J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics,2007,37(3):713-719.
[122]Liu. H. Y., Zhao, L. Zhang, Z. X., Ou Y. Stochastic stability of Markovian jumping Hopfield neural networks with constant and distributed delays. Neurocomputing 2009:72(16-18):3669-3676.
[123]Wang, G. J., Cao, J. D., Xu, M., Stability Analysis for Stochastic BAM Neural Networks with Markovian Jumping Parameters [J], Neurocomputing,2009, 72(16-18):3901-3906.
[124]Han. W., Liu,Y., Wang, L.S., Robust Exponential Stability of Markovian Jumping Neural Networks with Mode-dependent Delay[J]. Communications in Nonlinear Science and Numerical Simulation.2010,15(9):2529-2535.
[125]Li, H.Y., Chen. B., Zhou, Q. Lin, C., Robust Exponential Stability for Delayed Uncertain Hopfield Neural Networks with Markovian Jumping Parameters [J]. Physics Letters A,2008,372(30):4996-5003.
[126]Ei-Sayed, M. L., Krishnaprasad, P. S., Homogenous Interconnected Systems:A Example [J]. IEEE Transaction Automatic Control,1981,26(4):894-901.
[127]Davison, E. J., Tripathi, N., The Optimal Decentralized Control of a Large Power System:Load and Frequence control [J]. IEEE Transaction Automatic Control,1978, 23(2):312-325.
[128]Barbieri, E., Stability Analysis of a Class of Interconnected Systems [J]. ASME Journal of Dynamic System, Measurements, Control,1993,115(3):546-551.
[129]Siljak, D. D., Large-scale Dynamic Systems Stability and Structure [M]. North-Holland:Amstrerdam,1978.
[130]文海霞.一类时滞非线性动力系统的全局指数稳定性[J].科学技术与工程,2009.9(2)：430-433.
[131]张继业,杨翊仁,曾京.无限维关联系统的弦稳定性[J].应用数学和力学,2000,21(7)：715-719.
[132]Liu, B., Teo, K. L., Liu, X. Z., Robust Exponential Stabilization for Large-scale Uncertain Impulsive Systems with Coupling Time-delays [J]. Nonlinear Analysis. 2008,68(5):1169-1183.
[133]Pant, A., Mesh Stability of Look-ahead Interconnected Systems [J]. IEEE Transaction on Automatic Control,2003,47(2):403-408.
[134]Khasminski, R. Z., Stochastic Stability of Differential Equations [M]. Groningen. The Netherlands:Sijthoff & Noordhoff,1980.
[135]Slotine, J. E., Li, W. P.,应用非线性控制[M].北京：机械工业出版社,2004.
[136]任殿波,张策,张继业.考虑前后信息的车辆跟随自适应控制[J].哈尔滨工业大学学报.2011,43(6)：76-80.
[137]任殿波,张京明,张继业.具有不确定参数的车辆跟随滑模控制[J].电机与控制学报.2010,14(1)：73-77.
[138]Niu,Y. G., Ho, W.C. D., Robust Observer Design for Ito Stochastic Time-delay Systems via Sliding Mode Control [J]. Systems & Control Letters,2006,55(10): 781-793.
[139]Higham, D. J., An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations [J]. Society for Industrial and Applied Mathematics.2001, 43(3):525-546.