不确定非线性系统的鲁棒滑模控制方法研究
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摘要
在实际的工业过程中，系统通常具有非线性、时变性、不确定性等其它复杂特性，时滞现象也是普遍存在于实际的工业生产过程中，这使得非线性系统的控制问题变得具有挑战性。因此，带有不确定性和时滞的非线性系统的鲁棒滑模控制方法研究越来越受到重视和关注。论文针对带有不确定性和时滞的非线性系统，基于线性矩阵不等式技术、自适应技术和神经网络技术、Backstepping技术、鲁棒控制方法、有限时间控制方法，研究非线性系统控制问题。论文的主要内容分以下几部分：
针对不确定一致混沌系统，基于有限时间控制方法和Lyapunov稳定性理论，设计鲁棒反馈同步控制器，使得主从系统有限时间同步；针对未知参数不确定混沌系统，基于有限时间控制方法，给出带积分项的滑模面，并利用自适应参数辨识技术估计未知参数，进而基于Lyapunov稳定性理论，设计自适应滑模控制器，使得主从系统有限时间同步。
针对带有外部扰动的不确定非线性中立系统，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定；针对带有外部扰动的不确定非线性中立系统，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定，给出不带时滞项的滑模面，进而基于Lyapunov稳定性理论，设计了鲁棒滑模控制器，使得闭环系统一致渐近稳定。
针对时变时滞细胞神经网络，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定；针对非仿射非线性系统，利用神经网络对非线性系统进行辨识，并利用自适应参数辨识估计神经网络权值系数，进而基于Lyapunov稳定性理论，设计神经网络自适应滑模控制器，从而实现闭环系统一致渐近有界稳定；针对带有时滞的非仿射非线性系统，利用神经网络对非线性系统进行辨识，并利用自适应算法调整神经网络的权值系数，进而基于Lyapunov稳定性理论，设计基于Backstepping控制策略的神经网络自适应滑模跟踪器，使系统状态能够跟踪上预设轨迹。
针对带有匹配扰动的离散非线性系统，给出滑模函数，并基于Lyapunov稳定性理论，设计非线性滑模控制器，进而利用矩阵技巧解出控制器参数，进一步利用Newton-Raphson算法解出控制器输入，从而使系统状态稳定在很小的临域内，并消除了抖振；针对不确定时变时滞离散非线性切换系统，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定，给出不带时滞项的滑模面，进而基于Lyapunov稳定性理论，设计非线性鲁棒滑模控制器，进一步利用Newton-Raphson算法解出控制器输入，从而实现闭环系统一致渐近稳定。
Man-made systems with advanced functionalities in practical industrial processesusually exhibit nonlinearities, time-varying, unpredictable parameters and othercomplexities from design limitation, operation conditions, integrated inherent dynamics,even internal and external disturbances. In addition, delay is also common phenomenonencountered in the actual industrial production process, which makes the control systemdesign even challenging. Therefore, the robust sliding mode control method for uncertainnonlinear systems with time delay has attracted greater attention. In the thesis, theproblems of robust sliding mode control method for uncertain nonlinear systems withtime delay are studied by using linear matrix inequality, adaptive，backstepping andneural network, robust control and finite time control methods. A brief introduction of themajor research contents and achievement is outlined below.
Firstly, it studies unified chaotic systems with uncertain parameters, and the robustfeedback synchronization controller is designed based on finite time control method andLyapunov stability theory, in order to achieve finite time synchronization between themaster and slave systems. Secondly, it studies chaotic systems with unknown parametersand uncertainties, the integral sliding mode surface proposed based on finite time controlmethod, the unknown parameters estimated by adaptive technique, the adaptive slidingmode synchronization controller is designed based on Lyapunov stability theory, in orderto achieve finite time synchronization between the master and slave systems.
Firstly, it studies nonlinear neutral systems with uncertain parameters and externaldisturbance, the new robust stability criterion is provided in the form of linear matrixinequality based on Lyapunov stability theory, the system uncertainties are disposed bymatrix inequality technique. Secondly, it studies nonlinear neutral systems with uncertainparameters and external disturbance, the new robust stability criterion is provided in theform of linear matrix inequality based on Lyapunov stability theory, the systemsuncertainties were disposed by matrix inequality technique, the new sliding mode surfacewithout time delay term is designed, the robust sliding mode controller designed based on Lyapunov stability theory, in order to achieve uniformly asymptotic stability of theclosed-loop systems.
Firstly, it studies cellular neural networks with uncertain parameters andtime-varying delays, the robust stability criterion is provided in the form of linear matrixinequality based on Lyapunov stability theory. Secondly, it studies non-affine nonlinearsystems, the nonlinear systems identified by neural network technique, the weightingcoefficients of neural network are adjusted by adaptive technique, the adaptive neuralnetwork sliding mode controller is designed based on Lyapunov stability theory, in orderto achieved uniformly ultimately boundedness of the closed-loop systems. Thirdly, itstudies non-affine nonlinear systems with time delays, the nonlinear systems identifiedby neural network technique, the weighting coefficients of neural network are adjusted byadaptive technique, the adaptive neural network sliding mode controller is designedbased on Lyapunov stability theory, so that the system trajectories can track the set pointvalues.
Firstly, it studies discrete nonlinear systems with matching perturbations, the slidingfunction proposed, the nonlinear sliding mode controller is designed based on Lyapunovstability theory, the controller parameters obtained by matrix technique, the controllerinput obtained by Newton-Raphson Algorithm, in order to achieve uniformly asymptoticstability of the closed-loop system meanwhile eliminating the chattering effect,. Secondly,it studies discrete nonlinear switched systems with uncertain parameters and time-varyingdelays, the new robust stability criterion is provided in the form of linear matrixinequality based on Lyapunov stability theory, the systems uncertainties were disposedby matrix inequality technique, the new sliding mode surface without time delay term isdesigned, the robust sliding mode controller designed based on Lyapunov stability theory,the controller input obtained by Newton-Raphson Algorithm in order to achieveuniformly asymptotic stability of the closed-loop system.
针对不确定一致混沌系统，基于有限时间控制方法和Lyapunov稳定性理论，设计鲁棒反馈同步控制器，使得主从系统有限时间同步；针对未知参数不确定混沌系统，基于有限时间控制方法，给出带积分项的滑模面，并利用自适应参数辨识技术估计未知参数，进而基于Lyapunov稳定性理论，设计自适应滑模控制器，使得主从系统有限时间同步。
针对带有外部扰动的不确定非线性中立系统，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定；针对带有外部扰动的不确定非线性中立系统，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定，给出不带时滞项的滑模面，进而基于Lyapunov稳定性理论，设计了鲁棒滑模控制器，使得闭环系统一致渐近稳定。
针对时变时滞细胞神经网络，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定；针对非仿射非线性系统，利用神经网络对非线性系统进行辨识，并利用自适应参数辨识估计神经网络权值系数，进而基于Lyapunov稳定性理论，设计神经网络自适应滑模控制器，从而实现闭环系统一致渐近有界稳定；针对带有时滞的非仿射非线性系统，利用神经网络对非线性系统进行辨识，并利用自适应算法调整神经网络的权值系数，进而基于Lyapunov稳定性理论，设计基于Backstepping控制策略的神经网络自适应滑模跟踪器，使系统状态能够跟踪上预设轨迹。
针对带有匹配扰动的离散非线性系统，给出滑模函数，并基于Lyapunov稳定性理论，设计非线性滑模控制器，进而利用矩阵技巧解出控制器参数，进一步利用Newton-Raphson算法解出控制器输入，从而使系统状态稳定在很小的临域内，并消除了抖振；针对不确定时变时滞离散非线性切换系统，基于Lyapunov稳定性理论，通过线性矩阵不等式形式给出鲁棒稳定性新判据，并利用矩阵不等式技巧处理系统的不确定，给出不带时滞项的滑模面，进而基于Lyapunov稳定性理论，设计非线性鲁棒滑模控制器，进一步利用Newton-Raphson算法解出控制器输入，从而实现闭环系统一致渐近稳定。
Man-made systems with advanced functionalities in practical industrial processesusually exhibit nonlinearities, time-varying, unpredictable parameters and othercomplexities from design limitation, operation conditions, integrated inherent dynamics,even internal and external disturbances. In addition, delay is also common phenomenonencountered in the actual industrial production process, which makes the control systemdesign even challenging. Therefore, the robust sliding mode control method for uncertainnonlinear systems with time delay has attracted greater attention. In the thesis, theproblems of robust sliding mode control method for uncertain nonlinear systems withtime delay are studied by using linear matrix inequality, adaptive，backstepping andneural network, robust control and finite time control methods. A brief introduction of themajor research contents and achievement is outlined below.
Firstly, it studies unified chaotic systems with uncertain parameters, and the robustfeedback synchronization controller is designed based on finite time control method andLyapunov stability theory, in order to achieve finite time synchronization between themaster and slave systems. Secondly, it studies chaotic systems with unknown parametersand uncertainties, the integral sliding mode surface proposed based on finite time controlmethod, the unknown parameters estimated by adaptive technique, the adaptive slidingmode synchronization controller is designed based on Lyapunov stability theory, in orderto achieve finite time synchronization between the master and slave systems.
Firstly, it studies nonlinear neutral systems with uncertain parameters and externaldisturbance, the new robust stability criterion is provided in the form of linear matrixinequality based on Lyapunov stability theory, the system uncertainties are disposed bymatrix inequality technique. Secondly, it studies nonlinear neutral systems with uncertainparameters and external disturbance, the new robust stability criterion is provided in theform of linear matrix inequality based on Lyapunov stability theory, the systemsuncertainties were disposed by matrix inequality technique, the new sliding mode surfacewithout time delay term is designed, the robust sliding mode controller designed based on Lyapunov stability theory, in order to achieve uniformly asymptotic stability of theclosed-loop systems.
Firstly, it studies cellular neural networks with uncertain parameters andtime-varying delays, the robust stability criterion is provided in the form of linear matrixinequality based on Lyapunov stability theory. Secondly, it studies non-affine nonlinearsystems, the nonlinear systems identified by neural network technique, the weightingcoefficients of neural network are adjusted by adaptive technique, the adaptive neuralnetwork sliding mode controller is designed based on Lyapunov stability theory, in orderto achieved uniformly ultimately boundedness of the closed-loop systems. Thirdly, itstudies non-affine nonlinear systems with time delays, the nonlinear systems identifiedby neural network technique, the weighting coefficients of neural network are adjusted byadaptive technique, the adaptive neural network sliding mode controller is designedbased on Lyapunov stability theory, so that the system trajectories can track the set pointvalues.
Firstly, it studies discrete nonlinear systems with matching perturbations, the slidingfunction proposed, the nonlinear sliding mode controller is designed based on Lyapunovstability theory, the controller parameters obtained by matrix technique, the controllerinput obtained by Newton-Raphson Algorithm, in order to achieve uniformly asymptoticstability of the closed-loop system meanwhile eliminating the chattering effect,. Secondly,it studies discrete nonlinear switched systems with uncertain parameters and time-varyingdelays, the new robust stability criterion is provided in the form of linear matrixinequality based on Lyapunov stability theory, the systems uncertainties were disposedby matrix inequality technique, the new sliding mode surface without time delay term isdesigned, the robust sliding mode controller designed based on Lyapunov stability theory,the controller input obtained by Newton-Raphson Algorithm in order to achieveuniformly asymptotic stability of the closed-loop system.
引文
[1] S. H. Zak. Systems and Control. New York, Oxford: Oxford University Press.2003
[2] Y.S. Xia, G. Feng, M. Kamel. Development and Analysis of a Neural Dynamical Approach toNonlinear Programming Problems. IEEE Trans. on Automatic control,2007,52(11):2154~2159
[3]苏宏业,褚健,鲁仁全.不确定时滞系统的鲁棒控制理论,北京:科学出版社,2007
[4] A. Polyakov, A. Poznyak.“Reaching Time Estimation for “Super-Twisting” Second OrderSliding Mode Controller via Lyapunov Function Designing.” IEEE Trans. Automatic Control,2009,54:1951~1955
[5]徐湘元.自适应控制理论与应用.北京:电子工业出版社,2006
[6]李文磊,张智焕,井元伟.基于自适应Backstepping设计的TCSC非线性鲁棒控制器.控制理论与应用,2005,22(1):153~160
[7] D. Lee, Y. Park, Y. Park. Robust H infinite Sliding Mode Descriptor Observer for Fault andOutput Disturbance Estimation of Uncertain Systems. IEEE Trans. Automatic Control,2012,57:2928~2934
[8] J. Kaloust, Z. Qu. Robust Control Design for Nonlinear Uncertain Systems with an UnknownTime-varying Control Direction. IEEE Trans. Automatic Control,1997,42:393~399
[9] R. Marino, P. Tomei. Global Adaptive Output-feedback Control of Nonlinear Systems. II.Nonlinear Parameterization. IEEE Trans. Automatic Control,1993,38:33~48
[10] Y.G. Hong, J.K. Wang, D.Z. Cheng. Adaptive Finite-time Control of Nonlinear Systems withParametric Uncertainty. IEEE Trans. Automatic Control,2006,51:858~862
[11] X.H. Jiao, T.L. Shen. Adaptive Feedback Control of Nonlinear Time-Delay Systems: TheLaSalle-Razumikhin-Based Approach. IEEE Trans. on Automatic Control,2005,50:1909~1913
[12] X.Q. Huang, W. Lin, B. Yang. Global Finite-Time Stabilization of a Class of UncertainNonlinear Systems. Automatica,2005,41:881~888
[13]张建华.基于细胞神经网络的非线性时滞系统自适应控制.燕山大学博士论文,2010
[14] K. P. Tee, S. S. Ge and E. H. Tay. Barrier Lyapunov Functions for the Control ofOutput-constrained Nonlinear Systems. Automatica,2009,45:918~927
[15] A. Donaire, S. Junco. On the Addition of Integral Action to Port-controlled HamiltonianSystems. Automatica,2009,45:1910~1916
[16] F. Castanos, R. Ortega, A. Schaft. Asymptotic Stabilization via Vontrol by Interconnection ofPort-Hamiltonian Systems. Automatica,2009,45:1611~1618
[17] X. L. Wang, Y. G. Hong, Z. P. Jiang. Finite-Time Input-to-State Stability and Optimization ofSwitched Systems. Proceedings of the27th Chinese Control Conference,2008,7:16~18
[18] P. Myszkorowski, U. Holmberg. Comments on “Variable structure control design for uncertaindiscrete-time systems”. IEEE Trans. Automatic Control,1994,39:2366~2367
[19] W. J. Wang, G. H. Wu, D. C. Yang. Variable Structure Control Design for UncertainDiscrete-Time Systems. IEEE Trans. Automatic Control,1994,39:99~102
[20] S. K Spurgeon. Hyper Plane Design Techniques for Discrete-Time Variable Structure ControlSystems. International Journal of Control.1992,55:445~456
[21] I. V. Utkin. Variable Structure Systems with Sliding Modes. IEEE Trans. Automatic Control,1977,22:212~222
[22] A. Levant. Robust Exact Differentiation via Sliding Mode Technique. Automatica,1998,34:379~384
[23] G. Bartolini, A. Pisano, E. Punta, E. Usai. A Survey of Application of Second-Order SlidingMode Control to Mechanical Systems. International Journal of Control.2003,76:875~982
[24] A. Levant. Sliding Order and Sliding Accuracy in Sliding Mode Control. International Journalof Control,2003,58:1247~1263
[25] A. Levant. Universal SISO Sliding-Mode Controllers with Finite-Tine Convergence. IEEETrans. Automatic Control,2001,46:1447~1451
[26] A. Levant. Higher Order Sliding Modes, Differentiation and Output-Feedback Control.International Journal of Control,2003,76:924~941
[27] A. Levant. Quasi-Continuous High-Order Sliding-Mode Controllers. IEEE Trans. AutomaticControl,2005,50:1812~1816
[28] T. L. Chern, C.W. Chuang, R.L. Jiang. Design of Discrete Integral Variable Structure ControlSystems and Application to a Brushless DC Motor Control. Automatica,1996,32:5773~779
[29] Y. S. Liu. Robust Adaptive Observer for Nonlinear Systems with Unmodeled Dynamics,Automatica,2009,45:1891~1895
[30] J. P. Barbot, D. Boutat, T. Floquet. An Observation Algorithm for Nonlinear Systems withUnknown Inputs. Automatica,2009,45:1970~1974
[31] J. H. Park. Robust Guaranteed Cost Control for Uncertain Linear Differential Systems ofNeutral Type. Applied Mathematics and Computation,2003,140:523~535
[32] D. Zhang, L. Yu, Exponential Stability Analysis for Neutral Switched Systems with IntervalTime-Varying Mixed Delays and Nonlinear Perturbations, Nonlinear Analysis: Hybrid Systems,Nonlinear Analysis: Hybrid Systems,2012(6):775~786
[33] C.A.S. Batista, S.R. Lopes, R.L. Viana. Delayed Feedback Control of Bursting Synchronizationin a Scale-free Neuronal Network. Neural Networks,2010,23:114~124
[34] P. Colet, R. Roy. Digital Communication with Synchronized Chaotic Lasers. Opt Let.1994,19:2056~2058
[35] T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu. Observation of Synchronization inLaser Chaos. Phys Rev Lett.1994,72:3502~3506
[36] J.N. Lu, X.Q. Wu, J.H. Lu Synchronization of a Unified System and the Application in SecureCommunication. Phys Lett A,2002,305:365~370
[37] W. He, J. Cao. Generalized Synchronization of Chaotic Systems: an Auxiliary SystemApproach via Matrix Measure. Chaos.2009,19~23
[38] H. Wang, Z. Z. Han, Q. Y. Xie, W. Zhang. Finite-Time Chaos Synchronization of UnifiedChaotic System with Uncertain Parameters. Nonlinear Sci Numer Simulat.2009,14:2239~2247
[39] J. Huang, L.N. Sun, Z.Z. Han, L.P. Liu. Adaptive Terminal Sliding Mode Control for NonlinearDifferential Inclusion Systems with Disturbance. Nonlinear Dyn.,2013,72:221~228
[40] X.Wei, H.P. Yu. Second-Order Terminal Sliding Mode Controller for a Class of ChaoticSystems with Unmatched Uncertainties. Commun Nonlinear Sci Numer Simulat.2010,15:3241~3247
[41] W. Xiang, F.Q. Chen. An Adaptive Sliding Mode Control Scheme For A Class Of ChaoticSystems With Mismatched Perturbations And Inpur Nonlinearities. Commun Nonlinear SciNumer Simulat.2011,16:1~9
[42] X.L. Wu, Y. Li, J.H. Zhang. Synchronisation of Unified Chaotic Systems with UncertainParameters In Finite Time. Int. J. Modelling, Identification and Control.2012,17:295~301
[43] C. C. Fuh. Optimal Control of Chaotic Systems with Input Saturation Using an Input-StateLinearization Scheme. Commun Nonlinear Sci Numer Simulat.2009,143424~3431
[44] J.M.V. Grzybowski, M. Rafikov, J.M. Balthazar. Synchronization of The Unified ChaoticSystem and Application in Secure Communication. Commun Nonlinear Sci Numer Simulat.2009,14:2793~2806
[45] M. Rafikov, J.M. Balthazar. On Control and Synchronization in Chaotic and HyperchaoticSystems via Linear Feedback Control. Commun Nonlinear Sci Numer Simulat.2008,13:1246~1255
[46] U.E.Vincent, R.Guo. Finite-Time Synchronization for a Class of Chaotic and HyperchaoticSystems via Adaptive Feedback Controller. Phys Lett A.2011,375:2322~2326
[47] J. Zhou, J. E. Meng. Adaptive Output Control of a Class of Uncertain Chaotic Systems.Systems Control Letters.2007,56:452~460
[48] Z.o Lu, L.S. Shieh, G.R.Chen. Adaptive Feedback Linearization Control Of Chaotic Systemsvia Recurrent High-Order Neural Networks. Information Sciences.2006,176:2337~2354
[49] Y. G. Yua, H.X. Li. Adaptive Hybrid Projective Synchronization of Uncertain Chaotic SystemsBased on Backstepping Design. Nonlinear Analysis: Real World Applications2011,12:388~393
[50] H.H. Chen, G.J. Sheu, Y. L. Lin, C. S. Chen. Chaos Synchronization between Two DifferentChaotic Systems via Nonlinear Feedback Control. Nonlinear Analysis: Theory, Methods&Applications.2009,70:4393~4401
[51] B. Wang, G.J. Wen. On The Synchronization of a Class of Chaotic Systems based onBackstepping Method. Phys Lett A.2007,370:35~39
[52] M.T. Yassen. Controlling, Synchronization and Tracking Chaotic Liu System Using ActiveBackstepping Design. Phys Lett A.2007,360:582~587
[53] M. Pourmahmood, S. Khanmohammadi, G. Alizadeh. Synchronization of Two DifferentUncertain Chaotic Systems with Unknown Parameters Using a Robust Adaptive Sliding ModeController. Commun. Nonlinear Sci. Numer. Simulat.2011,16:2853~2868
[54] M. P. Aghababa, S. Khanmohammadi, G. Alizadehj. Finite-Time Synchronization of TwoDifferent Chaotic Systems with Unknown Parameters via Sliding Mode Technique. AppliedMathematical Modelling.2011,35:3080~3091
[55] Y. Chen, R.R. Hwang, C. Chang. Adaptive Impulsive Synchronization of Uncertain ChaoticSystems. Phys. Lett. A.2010,374:2254~2258
[56] Y. Yu, S. Zhang. Adaptive Backstepping Synchronization of Uncertain Chaotic System. ChaosSoliton Fract.2004,21:643~649
[57] C. Wang, S.S. Ge. Adaptive Synchronization of Uncertain Chaotic Systems via BachsteppingDesign. Chaos Soliton Fract.2001,12:1199~1206
[58] A. E. Gohary, A. Sarhan. Optimal Control and Synchronization of Lorenz System withComplete Unknown Parameters. Chaos Soliton Fract.2006,30:1122~1132
[59] A. E. Gohary. Optimal Synchronization of Rossler System with Complete UncertainParameters. Chaos Soliton Fract.2006,27:345~355
[60] J. Lu, J. Cao. Adaptive Complete Synchronization of Two Identical or Different Chaotic(Hyperchaotic) Systems with Fully Unknown Parameters. Chaos.2005,15
[61] X. Chen, J. Lu. Adaptive Synchronization of Different Chaotic Systems with Fully UnknownParameters. Phys. Lett. A.2007,364:123~128
[62] H. Zhang, W. Huang, Z. Wang, T. Chai. Adaptive Synchronization between Two DifferentChaotic Systems with Unknown Parameters. Phys. Lett. A.2006,350:363~366
[63] H. Chen. Stability Criterion for Synchronization of Chaotic Systems Using Linear FeedbackControl. Phys. Lett. A.2008,372:1841~1850
[64] L. Zhang, L. Huang, Z. Zhang, Z. Wang. Fuzzy Adaptive Synchronization of Uncertain ChaoticSystems via Delayed Feedback Control. Phys. Lett. A.2008,372:6082~6086
[65] J. Kim, C. Park, E. Kim, M. Park. Fuzzy Adaptive Synchronization of Uncertain ChaoticSystems. Phys. Lett. A.2005,334:295~305
[66] E. Hwang, C. Hyun, E. Kim, M. Park. Fuzzy Model Based Adaptive Synchronization ofUncertain Chaotic Systems: Robust Tracking Control Approach. Phys. Lett. A.2009,373:1935~1939
[67] W. L. Li, K. M. Chang. Robust Synchronization of Drive-Response Chaotic Systems viaAdaptive Sliding Mode Control. Chaos Soliton Fract.2009,39:2086~2092
[68] H. Kebriaei, M. J. Yazdanpanah. Robust Adaptive Synchronization of Different UncertainChaotic Systems Subject to Input Nonlinearity. Commun Nonlinear sci. Numer. Simulat.2010,15:430~441
[69] M. Pourmahmood, S. Khanmohammadi, G. Alizadeh. Finite-Time Synchronization of TwoDifferent Chaotic Systems with Unknown Parameters via Sliding Mode Technique. AppliedMathematical Modelling.2011,35:3080~3091
[70] W. Perruquetti, T. Floquet, E. Moulay. Finite-Time Observers: Application to SecureCommunication. IEEE Trans. Automat. Control.2008,53:356~360
[71] H. Wang, Z.Z. Han, Q. Y. Xie, W. Zhang. Finite-Time Chaos Synchronization of UnifiedChaotic System with Uncertain Parameters. Commun Nonlinear Sci Numer Simulat.2009,14:2239~2247
[72] W. Yu. Finite-Time Stabilization of Three-Dimensional Chaotic Systems Based on CLF. Phys.Lett. A.2010,374:3021~3024
[73] H. Wang, Z. Han, Qi. Xie, W. Zhang. Sliding Mode Control for Chaotic Systems Based onLMI. Commun. Nonlinear Sci Numer. Simulat.2009,14:1410~1417
[74] W. Xiang, Y. Huangpu. Second-Order Terminal Sliding Mode Controller for a Class of ChaoticSystems with Unmatched Uncertainties. Commun. Nonlinear Sci. Numer. Simulat.2010,15:3241~3247
[75] H. Wang, Z. Han, Q. Xie, W. Zhang. Finite-Time Chaos Control via Nonsingular TerminalSliding Mode Control. Commun. Nonlinear Sci. Numer. Simulat.2009,14:2728~2733
[76] S. Li, Y. Tian. Finite-Time Synchronization of Chaotic Systems. Chaos Soliton Fract.2003,15:303~310
[77] H. Wang, Z. Han, Q. Xie, W. Zhang. Finite-Time Synchronization of Uncertain UnifiedChaotic Systems Based on CLF. Nonlinear Anal. RWA.2009,15:2842~2849
[78] H. Wang, Z. Han, Q. Xie, W. Zhang, Finite-Time Chaos Synchronization of Unified ChaoticSystem with Uncertain Parameters. Commun. Nonlinear Sci. Numer. Simulat.2009,14:2239~2247
[79] T. Gonzalez, J. A. Moreno, L. Fridman. Variable Gain Super-Twisting Sliding Mode Control.IEEE Trans. Automatic Control.2012,57:2100~2105
[80] T. Gonzalez, J. A. Moreno, L. Fridman,“Variable Gain Super-Twisting Sliding ModeControl,” IEEE Trans. Automatic Control,2012,57(8):2100~2105
[81] S. Z. Sarpturk, Y. Istefanopulos, O. Kaynak. On The Stability of Discrete-Time Sliding ModeControl Systems. IEEE Trans. Automatic Control,1987,32:930~932
[82] C. C. Cheng, M. H Lin, J. M. Hsiao. Sliding Mode Controllers Design for Linear Discrete-TimeSystems with Matching Perturbations. Automatica,2000,36:1205~1211
[83] J. A. Moreno, M. Osorio. Strict Lyapunov Functions for the Super-Twisting Algorithm. IEEETrans. Automatic Control.2012,57:1035~1040
[84] Q. L. Han. Improved Stability Criteria and Controller Design for Linear Neutral Systems.Automatica.2009,45:1948~1952
[85] N. Luo, D. L. M. Sen. State Feedback Sliding-Mode Control of a Class of UncertainTime-Delay Systems. IEE Proc. Control Theory Appl.1993,140:261~274
[86] M.S.Yang, P. L. Liu, H.C. Lu, Output Feedback Stabilization of Uncertain Dynamic SystemsWith Multiple State Delays via Sliding-Mode Control Strategy. Proc. IEEE Int. Symp. onIndustrial Electronics (ISIE) Conf. Bled. Slovenia.1999:1147~1152
[87] J. Hu, J. Chu, H. Su. SMVSC for a Class of Time-Delay Uncertain Systems with MismatchingUncertainties. IEE Proc., Control Theory Appl.2000,147:687~693
[88] D. Zhang, L. Yu. Exponential Stability Analysis for Neutral Switched Systems with IntervalTime-Varying Mixed Delays and Nonlinear Perturbations, Nonlinear Analysis: HybridSystems,2012,6:775~786
[89] F. Qiu, B.T. Cui, Y. Ji. Further Results On Robust Stability of Neutral System with MixedTime-Varying Delays and Nonlinear Perturbations, Nonlinear Analysis: Real WorldApplications,2010,11:895~906
[90] R. Sakthivel, K. Mathiyalagan S. Marshal Anthoni. Robust Stability and Control for UncertainNeutral Time Delay Systems. International Journal of Control.2012,85:373~383
[91] H.Y. Shao. Improved Delay-Dependent Stability Criteria for Systems with a Delay Varying ina Range. Automatica.2008,44:3215~3218
[92] K Moezzi, A. G. Aghdam. Adaptive Robust Control of Uncertain Neutral Time-Delay Systems.American Control Conference, Seattle, WA,2008:5162~5167.
[93] W.A Zhang, L.Yu. Delay-Dependent Guaranteed Cost Control for Uncertain Neutral Systemswith Nonlinear Parameter Perturbations. IET Control Theory Applications,2007,1:675~681.
[94] U. Baser, B. Kizilsac. Dynamic Output Feedback H Infinite Control Problem for Linear NeutralSystems. IEEE Transactions on Automatic Control2007,52:1113~1118
[95] Y.C. Lin, C.L. Lin. Optimal Control Approach for Robust Control Design of Neutral Systems.Optimal Control Applications&Methods,2009,30:87~102.
[96] M.V. Basin, L.M. Fridman, G. J. G. Rodriguez, P. Acosta. Optimal and Robust Sliding ModeControl for Linear Systems with Multiple Time Delays in Control Input. Asian Journal OfControl2003,5:557~567
[97] L.G. Wua, C.H. Wang, Q.S. Zeng, Observer-Based Sliding Mode Control for a Class ofUncertain Nonlinear Neutral Delay Systems Journal Of The Franklin Institute,2008(345):233~253
[98] Y. Niu, J. Lam, X. Wang. Sliding-Mode Control for Uncertain Neutral Delay Systems. IEEProc. Control Theory Appl.2004,151:38~44
[99] S. C. Qu, Z. Q. Lei, Q. M. Zhu, H. Nouri. Stabilization for a Class of Uncertain Multi-TimeDelays System Using Sliding Mode Controller. International Journal Of Innovative Computing,Information And Control.2011,7:4195~4205
[100] Y. G. He, L. Zhao, M.Y. Zhang. Advanced in Control Engineeringand Information ScienceSliding Mode Control for a class of Uncertain Neutral Delay Systems. Procedia Engineering.2011,15:1181~1185
[101] L.O.Chua, L.Yang. Cellular Neural Networks: Theory, IEEE Trans. Circuits Syst.1988,35:1257~1272
[102] J. D. Gao, J. Wang. Global Asymptotic and Robust Stability of Recurrent Neural Networkswith Delays. Circuits and Systems I.2005,52:417~426
[103] V. Singh. Improved Global Robust Stability of Interval Delayed Neural Networks via SplitInterval: Generalizations. Applied Mathematics and Computation.2008,20:290~297
[104] H. Gao, T. Chen. New Results on Stability of Discrete-Time Systems with Time-Varying StateDelay. IEEE Transactions on Automatic Control.2007,52:328~334
[105] W. D. Chang, R. C. Hwang, J. G. Hsieh, Application of an Auto-Tuning Neuron to SlidingMode Control, IEEE Transactions on Systems, Man And Cybernetics-Part C:Aplications AndRevises,2002,32(4):517:522
[106] T. C. Kuo, Y. J. Huang, S. H. Chang. Sliding Mode Control with Self-Tuning Law forUncertain Nonlinear System. ISA Transactions,2008,47:171~178
[107] C. C. Hua, S. X. Ding, X.P. Guan. Robust Controller Design for Uncertain Multiple-DelaySystems with Unknown Actuator Parameters. Automatica,2011,48:211~218
[108] D. J. Rubio, W. Yu. Nonlinear System Identification with Recurrent Neural Networks andDead-Zone Kalman Filter Algorithm. Neurocomputing.2007,70:2460~2466.
[109] I. Salgado, I. Chairez. Nonlinear Discrete Time Neural Network Observer. Neurocomputing,2013,101:73~81
[110] D. J. Rubio, W. Yu. Stability Analysis of Nonlinear System Identification via Delayed NeuralNetworks. IEEE Transactions On Circuits And Systems II: Express Briefs,2007,54:161~165
[111] S. S. Ge, F. Hong, T.H. Lee. Robust Adaptive Control of Nonlinear Systems with UnknownTime Delays. Automatica.2005,41:1181~1190
[112] S. S. Ge, G. Li, T. Lee. Adaptive NN Control for a Class of Strict-Feedback Discrete-TimeNonlinear Systems. Automatica.2003,39:807~819
[113] D. Wang, J. Huang. Adaptive Neural Network Control for a Class of Uncertain NonlinearSystems in Pure-Feedback Form. Automatica.2002,38:1365~1372
[114] G. Bartolini, E. Punta. Sliding Mode Output-Feedback Stabilization of Uncertain NonlinearNonaffine Systems. Automatica.2012,48:3106~3113
[115] T. Zhang, S. Ge, C. Hang. Design and Performance Analysis of a Direct Adaptive Controllerfor Nonlinear Systems. Automatica.1999,35:1809~1817
[116] T. Zhang, S. Ge. Adaptive Neural Control of MIMO Nonlinear State Time-Varying DelaySystems with Unknown Dead-Zones and Gain Signs. Automatica.2007,43:1021~1033
[117] N. Noroozi, M. Roopaei, M. Z. Jahromi. Adaptive Fuzzy Sliding Mode Control Scheme forUncertain Systems. Communications in Nonlinear Science and Numerical Simulation.2009,14:3978~3992
[118] W.Yu. Nonlinear System Identification Using Discrete-Time Recurrent Neural Networks withStable Learning Algorithms. Information Sciences.2004,158:131~147
[119] C. Yang, S.S. Ge, T.H. Lee. Output Feedback Adaptive Control of a Class of NonlinearDiscrete-Time Systems with Unknown Control Directions. Automatica.2009,45:270~276
[120] U. Romero. Neural Network Design and Model Reduction Approach for Black Box NonlinearSystem Identification with Reduced Number of Parameters. Neurocomputing.2013,101:170~180
[121] K. P. Tee, S. S. Ge, E. H. Tay. Barrier Lyapunov Functions for the Control ofOutput-Constrained Nonlinear Systems. Automatica.2009,45:918~927
[122] S.S.Ge, C. Wang. Direct Adaptive NN Control of a Class of Nonlinear Systems. IEEETransactions on Neural Networks.2002,13:214~221
[123] X. L. Wu, J. H. Zhang, Q. M. Zhu. A Generalized Procedure in Designing Recurrent NeuralNetwork Identification and Control of Time-Varying-Delayed Nonlinear Dynamic Systems.Neurocomputing.2010,73:1376~1383
[124] F. L. Lewis, A. Yesildirek, K. Liu. Multilayer Neural-Net Robot Controller with GuaranteedTracking Performance. IEEE Transactions on Neural Networks,1996,7:388~399
[125] M. Wu, S. S. Ge, K. S. Han. Approximation-Based Adaptive Tracking Control ofPure-Feedback Nonlinear Systems with Multiple Unknown Time-Varying Delays. IEEETransactions On Neural Networks,2010,21(11):1804~1816
[126] W. Yu. Multiple Recurrent Neural Networks for Stable Adaptive Control. Neurocomputing,2006,70:430~444
[127] V. Utkin. Sliding Mode in Control and Optimization. Berlin: Springer-Verlag,1992
[128] G. Bartolini, A. Pisano, E. Punta, E. Usai. A Survey of Application of Second-Order SlidingMode Control to Mechanical Systems. International Journal of Control.2003,76:875~982
[129] A. Pisano, A. Davila, L. Fridman, E. Usai. Cascade Control of PM DC Drives viaSecond-Order Sliding-Mode Technique. IEEE Transactions on Industrial Electronics.2008,55:3846~3854
[130] A. Ferrara, L. Magnani. Motion Control of Rigid Robot Manipulators via First and SecondOrder Sliding Modes. Journal of Intelligent Robot Systems.2007,48:23~36
[131] C. C. Cheng, M. H. Lin, J. M. Hsiao. Sliding Mode Controllers Design for LinearDiscrete-Time Systems with Matching Perturbations. Automatica.2000,36:1205~1211
[132] N. O. Lai, C. Edwards, S. K. Spurgeon. On Output Tracking Using Dynamic Output FeedbackDiscrete-Time Sliding-Mode Controllers. IEEE Trans. Automatic Control.2007.52:1975~1981
[133] P. Ignaciuk, A. Bartoszewicz. LQ Optimal Sliding Mode Supply Policy for Periodic ReviewInventory Systems. IEEE Trans. Automatic Control.2010,55:269~274
[134] T. Yoshimura. Adaptive Discrete Sliding Mode Control for Mechanical Systems withMismatched Uncertainties. Journal of Vibration and Control.2010,16:1417~1437
[135] Y. Pan, K. Furuta. Vss Control Design for Discrete-Time System. Control-Theory AndAdvanced Technology, Part1,1994,10:669~687
[136] Q. M. Zhu, L. Z. Guo. A Pole Placement Controller for Non-Linear Dynamic Plants. Proc InstnMech Engrs Part I: J Systems and Control Engineering.2010,216:467~476
[137] C. J. Taylor, A. Chotai, P.C. Young. Non-Linear Control by Input-Output State VariableFeedback Pole Assignment. International Journal of Control.2009,82:1029~1044
[138] O. M. Ghezawi, A. S. I. Zinober, S. A. Billings. Analysis and Design of Variable StructureSystems Using a Geometric Approach. International Journal of Control.1983,38:657~671
[139] K. Gu, V.L. Kharitonov, J. Chen. Stability of Time-Delay Systems, Springer-Verlag, Berlin,Germany.2003
[140] V.N. Phat. Switched Controller Design For Stabilization of Nonlinear Hybrid Systems WithTime-Varying Delays In State And Control. Journal of the Franklin Institute.2010,347:195~207
[141] T. Li, A. Song, M. Xue, H. Zhang. Stability Analysis On Delayed Neural Networks Based OnAn Improved Delay-Partitioning Approach. Journal of Computational and AppliedMathematics.2011,235:3086~3095
[142] M. Wu, Y. He, J. She, G. Liu. Delay-Dependent Criteria for Robust Stability of Time-VaryingDelay Systems. Automatica.2004,40:1435~1439
[143] Y. He, M. Wu, G. Liu, J. She. Output Feedback Stabilization for A Discrete-Time System WithA Time-Varying Delay. IEEE Transactions on Automatic Control.2008,53:2372~2377
[144] P. Shi, M.S. Mahmoud, J. Yi, A. Ismail. Worst Case Control of Uncertain Jumping Systemswith Multi-State and Input Delay Information. Information Sciences.2006,176:186~200
[145] Y. Xia, Z. Zhu, C. Li, H. Yang, Q. Zhu. Robust Adaptive Sliding Mode Control For UncertainDiscrete-Time Systems With Time Delay. Journal of the Franklin Institute.2010,347:339~357
[146] F. Gouaisbaut, D. Peaucelle. Delay-Dependent Stability Analysis Of Linear Time DelaySystems, In: IFAC Workshop On Time Delay System, L’Aquila, Italy, January2006
[147] Z. Feng, J. Lam, H. Gao, B. Du. Improved Stability and Stabilization Results for DiscreteSingular Delay Systems via Delay Partitioning, In: IEEE Conference on Decision and Controland28th Chinese Control Conference, Shanghai, China,2009
[148] G. Zhai, I. Matsune, J. Imae, T. Kobayashi. A Note on Multiple Lyapunov Functions andStability Condition for Switched and Hybrid Systems. International Journal of InnovativeComputing, Information and Control.2009,5:1189~1199
[149] R. Wang, J. Zhao. Exponential Stability Analysis for Discrete-Time Switched Linear Systemswith Time-Delay. Information and Control.2007,3:1557~1564
[150] L. Wu, Z. Wang. Guaranteed Cost Control For Linear Switched Systems With Neutral Delayvia Dynamic Output Feedback. International Journal of Systems Science.2009,40:717~728
[151] W. Xiang, J. Xiao. H Infinite Finite-Time Control for Switched Nonlinear Discrete-TimeSystems with Norm-Bounded Disturbance. Journal of the Franklin Institute.2011,348:331~352
[152] W. Zhang, L. Yu, S. Yin. A Switched System Approach to H Infinite Control of NetworkedControl Systems with Time-Varying Delays. Journal of the Franklin Institute.2011,348:165~178
[153] L. Wu, J. Lam. Sliding Mode Control of Switched Hybrid Systems With Time-Varying Delay.International Journal of Adaptive Control and Signal Processing.2008,22:909~931
[154] M. Basin, A. Ferreira, L.M. Fridman. Sliding Mode Identification and Control For LinearUncertain Stochastic Systems. International Journal of Systems Science.2007,38:861~869
[155] S. Vaidyanathan. Hybrid Chaos Synchronization of Hyperchaotic Newton-Leipnik Systems bySliding Mode Control. International Journal of Control Theory and Computer Modelling.2011,1:1~10
[156] Y. Xia, Y. Jia. Robust Sliding-Mode Control For Uncertain Time-Delay Systems: An LMIApproach. IEEE Transactions on Automatic Control.2003,48:1086~1092
[157] Y. Niu, J. Lam, X. Wang. Sliding-Mode Control for Uncertain Neutral Delay Systems. IEEProceedings: Part D. Control Theory and Applications.2004,151:38~44
[158] X. X. Yu, C. F. Wu, F. Z. Liu. Sliding Mode Control of Discrete-Time Switched Systems withTime-Delay. Journal of the Franklin Institute.2013,350:19~33
[2] Y.S. Xia, G. Feng, M. Kamel. Development and Analysis of a Neural Dynamical Approach toNonlinear Programming Problems. IEEE Trans. on Automatic control,2007,52(11):2154~2159
[3]苏宏业,褚健,鲁仁全.不确定时滞系统的鲁棒控制理论,北京:科学出版社,2007
[4] A. Polyakov, A. Poznyak.“Reaching Time Estimation for “Super-Twisting” Second OrderSliding Mode Controller via Lyapunov Function Designing.” IEEE Trans. Automatic Control,2009,54:1951~1955
[5]徐湘元.自适应控制理论与应用.北京:电子工业出版社,2006
[6]李文磊,张智焕,井元伟.基于自适应Backstepping设计的TCSC非线性鲁棒控制器.控制理论与应用,2005,22(1):153~160
[7] D. Lee, Y. Park, Y. Park. Robust H infinite Sliding Mode Descriptor Observer for Fault andOutput Disturbance Estimation of Uncertain Systems. IEEE Trans. Automatic Control,2012,57:2928~2934
[8] J. Kaloust, Z. Qu. Robust Control Design for Nonlinear Uncertain Systems with an UnknownTime-varying Control Direction. IEEE Trans. Automatic Control,1997,42:393~399
[9] R. Marino, P. Tomei. Global Adaptive Output-feedback Control of Nonlinear Systems. II.Nonlinear Parameterization. IEEE Trans. Automatic Control,1993,38:33~48
[10] Y.G. Hong, J.K. Wang, D.Z. Cheng. Adaptive Finite-time Control of Nonlinear Systems withParametric Uncertainty. IEEE Trans. Automatic Control,2006,51:858~862
[11] X.H. Jiao, T.L. Shen. Adaptive Feedback Control of Nonlinear Time-Delay Systems: TheLaSalle-Razumikhin-Based Approach. IEEE Trans. on Automatic Control,2005,50:1909~1913
[12] X.Q. Huang, W. Lin, B. Yang. Global Finite-Time Stabilization of a Class of UncertainNonlinear Systems. Automatica,2005,41:881~888
[13]张建华.基于细胞神经网络的非线性时滞系统自适应控制.燕山大学博士论文,2010
[14] K. P. Tee, S. S. Ge and E. H. Tay. Barrier Lyapunov Functions for the Control ofOutput-constrained Nonlinear Systems. Automatica,2009,45:918~927
[15] A. Donaire, S. Junco. On the Addition of Integral Action to Port-controlled HamiltonianSystems. Automatica,2009,45:1910~1916
[16] F. Castanos, R. Ortega, A. Schaft. Asymptotic Stabilization via Vontrol by Interconnection ofPort-Hamiltonian Systems. Automatica,2009,45:1611~1618
[17] X. L. Wang, Y. G. Hong, Z. P. Jiang. Finite-Time Input-to-State Stability and Optimization ofSwitched Systems. Proceedings of the27th Chinese Control Conference,2008,7:16~18
[18] P. Myszkorowski, U. Holmberg. Comments on “Variable structure control design for uncertaindiscrete-time systems”. IEEE Trans. Automatic Control,1994,39:2366~2367
[19] W. J. Wang, G. H. Wu, D. C. Yang. Variable Structure Control Design for UncertainDiscrete-Time Systems. IEEE Trans. Automatic Control,1994,39:99~102
[20] S. K Spurgeon. Hyper Plane Design Techniques for Discrete-Time Variable Structure ControlSystems. International Journal of Control.1992,55:445~456
[21] I. V. Utkin. Variable Structure Systems with Sliding Modes. IEEE Trans. Automatic Control,1977,22:212~222
[22] A. Levant. Robust Exact Differentiation via Sliding Mode Technique. Automatica,1998,34:379~384
[23] G. Bartolini, A. Pisano, E. Punta, E. Usai. A Survey of Application of Second-Order SlidingMode Control to Mechanical Systems. International Journal of Control.2003,76:875~982
[24] A. Levant. Sliding Order and Sliding Accuracy in Sliding Mode Control. International Journalof Control,2003,58:1247~1263
[25] A. Levant. Universal SISO Sliding-Mode Controllers with Finite-Tine Convergence. IEEETrans. Automatic Control,2001,46:1447~1451
[26] A. Levant. Higher Order Sliding Modes, Differentiation and Output-Feedback Control.International Journal of Control,2003,76:924~941
[27] A. Levant. Quasi-Continuous High-Order Sliding-Mode Controllers. IEEE Trans. AutomaticControl,2005,50:1812~1816
[28] T. L. Chern, C.W. Chuang, R.L. Jiang. Design of Discrete Integral Variable Structure ControlSystems and Application to a Brushless DC Motor Control. Automatica,1996,32:5773~779
[29] Y. S. Liu. Robust Adaptive Observer for Nonlinear Systems with Unmodeled Dynamics,Automatica,2009,45:1891~1895
[30] J. P. Barbot, D. Boutat, T. Floquet. An Observation Algorithm for Nonlinear Systems withUnknown Inputs. Automatica,2009,45:1970~1974
[31] J. H. Park. Robust Guaranteed Cost Control for Uncertain Linear Differential Systems ofNeutral Type. Applied Mathematics and Computation,2003,140:523~535
[32] D. Zhang, L. Yu, Exponential Stability Analysis for Neutral Switched Systems with IntervalTime-Varying Mixed Delays and Nonlinear Perturbations, Nonlinear Analysis: Hybrid Systems,Nonlinear Analysis: Hybrid Systems,2012(6):775~786
[33] C.A.S. Batista, S.R. Lopes, R.L. Viana. Delayed Feedback Control of Bursting Synchronizationin a Scale-free Neuronal Network. Neural Networks,2010,23:114~124
[34] P. Colet, R. Roy. Digital Communication with Synchronized Chaotic Lasers. Opt Let.1994,19:2056~2058
[35] T. Sugawara, M. Tachikawa, T. Tsukamoto, T. Shimizu. Observation of Synchronization inLaser Chaos. Phys Rev Lett.1994,72:3502~3506
[36] J.N. Lu, X.Q. Wu, J.H. Lu Synchronization of a Unified System and the Application in SecureCommunication. Phys Lett A,2002,305:365~370
[37] W. He, J. Cao. Generalized Synchronization of Chaotic Systems: an Auxiliary SystemApproach via Matrix Measure. Chaos.2009,19~23
[38] H. Wang, Z. Z. Han, Q. Y. Xie, W. Zhang. Finite-Time Chaos Synchronization of UnifiedChaotic System with Uncertain Parameters. Nonlinear Sci Numer Simulat.2009,14:2239~2247
[39] J. Huang, L.N. Sun, Z.Z. Han, L.P. Liu. Adaptive Terminal Sliding Mode Control for NonlinearDifferential Inclusion Systems with Disturbance. Nonlinear Dyn.,2013,72:221~228
[40] X.Wei, H.P. Yu. Second-Order Terminal Sliding Mode Controller for a Class of ChaoticSystems with Unmatched Uncertainties. Commun Nonlinear Sci Numer Simulat.2010,15:3241~3247
[41] W. Xiang, F.Q. Chen. An Adaptive Sliding Mode Control Scheme For A Class Of ChaoticSystems With Mismatched Perturbations And Inpur Nonlinearities. Commun Nonlinear SciNumer Simulat.2011,16:1~9
[42] X.L. Wu, Y. Li, J.H. Zhang. Synchronisation of Unified Chaotic Systems with UncertainParameters In Finite Time. Int. J. Modelling, Identification and Control.2012,17:295~301
[43] C. C. Fuh. Optimal Control of Chaotic Systems with Input Saturation Using an Input-StateLinearization Scheme. Commun Nonlinear Sci Numer Simulat.2009,143424~3431
[44] J.M.V. Grzybowski, M. Rafikov, J.M. Balthazar. Synchronization of The Unified ChaoticSystem and Application in Secure Communication. Commun Nonlinear Sci Numer Simulat.2009,14:2793~2806
[45] M. Rafikov, J.M. Balthazar. On Control and Synchronization in Chaotic and HyperchaoticSystems via Linear Feedback Control. Commun Nonlinear Sci Numer Simulat.2008,13:1246~1255
[46] U.E.Vincent, R.Guo. Finite-Time Synchronization for a Class of Chaotic and HyperchaoticSystems via Adaptive Feedback Controller. Phys Lett A.2011,375:2322~2326
[47] J. Zhou, J. E. Meng. Adaptive Output Control of a Class of Uncertain Chaotic Systems.Systems Control Letters.2007,56:452~460
[48] Z.o Lu, L.S. Shieh, G.R.Chen. Adaptive Feedback Linearization Control Of Chaotic Systemsvia Recurrent High-Order Neural Networks. Information Sciences.2006,176:2337~2354
[49] Y. G. Yua, H.X. Li. Adaptive Hybrid Projective Synchronization of Uncertain Chaotic SystemsBased on Backstepping Design. Nonlinear Analysis: Real World Applications2011,12:388~393
[50] H.H. Chen, G.J. Sheu, Y. L. Lin, C. S. Chen. Chaos Synchronization between Two DifferentChaotic Systems via Nonlinear Feedback Control. Nonlinear Analysis: Theory, Methods&Applications.2009,70:4393~4401
[51] B. Wang, G.J. Wen. On The Synchronization of a Class of Chaotic Systems based onBackstepping Method. Phys Lett A.2007,370:35~39
[52] M.T. Yassen. Controlling, Synchronization and Tracking Chaotic Liu System Using ActiveBackstepping Design. Phys Lett A.2007,360:582~587
[53] M. Pourmahmood, S. Khanmohammadi, G. Alizadeh. Synchronization of Two DifferentUncertain Chaotic Systems with Unknown Parameters Using a Robust Adaptive Sliding ModeController. Commun. Nonlinear Sci. Numer. Simulat.2011,16:2853~2868
[54] M. P. Aghababa, S. Khanmohammadi, G. Alizadehj. Finite-Time Synchronization of TwoDifferent Chaotic Systems with Unknown Parameters via Sliding Mode Technique. AppliedMathematical Modelling.2011,35:3080~3091
[55] Y. Chen, R.R. Hwang, C. Chang. Adaptive Impulsive Synchronization of Uncertain ChaoticSystems. Phys. Lett. A.2010,374:2254~2258
[56] Y. Yu, S. Zhang. Adaptive Backstepping Synchronization of Uncertain Chaotic System. ChaosSoliton Fract.2004,21:643~649
[57] C. Wang, S.S. Ge. Adaptive Synchronization of Uncertain Chaotic Systems via BachsteppingDesign. Chaos Soliton Fract.2001,12:1199~1206
[58] A. E. Gohary, A. Sarhan. Optimal Control and Synchronization of Lorenz System withComplete Unknown Parameters. Chaos Soliton Fract.2006,30:1122~1132
[59] A. E. Gohary. Optimal Synchronization of Rossler System with Complete UncertainParameters. Chaos Soliton Fract.2006,27:345~355
[60] J. Lu, J. Cao. Adaptive Complete Synchronization of Two Identical or Different Chaotic(Hyperchaotic) Systems with Fully Unknown Parameters. Chaos.2005,15
[61] X. Chen, J. Lu. Adaptive Synchronization of Different Chaotic Systems with Fully UnknownParameters. Phys. Lett. A.2007,364:123~128
[62] H. Zhang, W. Huang, Z. Wang, T. Chai. Adaptive Synchronization between Two DifferentChaotic Systems with Unknown Parameters. Phys. Lett. A.2006,350:363~366
[63] H. Chen. Stability Criterion for Synchronization of Chaotic Systems Using Linear FeedbackControl. Phys. Lett. A.2008,372:1841~1850
[64] L. Zhang, L. Huang, Z. Zhang, Z. Wang. Fuzzy Adaptive Synchronization of Uncertain ChaoticSystems via Delayed Feedback Control. Phys. Lett. A.2008,372:6082~6086
[65] J. Kim, C. Park, E. Kim, M. Park. Fuzzy Adaptive Synchronization of Uncertain ChaoticSystems. Phys. Lett. A.2005,334:295~305
[66] E. Hwang, C. Hyun, E. Kim, M. Park. Fuzzy Model Based Adaptive Synchronization ofUncertain Chaotic Systems: Robust Tracking Control Approach. Phys. Lett. A.2009,373:1935~1939
[67] W. L. Li, K. M. Chang. Robust Synchronization of Drive-Response Chaotic Systems viaAdaptive Sliding Mode Control. Chaos Soliton Fract.2009,39:2086~2092
[68] H. Kebriaei, M. J. Yazdanpanah. Robust Adaptive Synchronization of Different UncertainChaotic Systems Subject to Input Nonlinearity. Commun Nonlinear sci. Numer. Simulat.2010,15:430~441
[69] M. Pourmahmood, S. Khanmohammadi, G. Alizadeh. Finite-Time Synchronization of TwoDifferent Chaotic Systems with Unknown Parameters via Sliding Mode Technique. AppliedMathematical Modelling.2011,35:3080~3091
[70] W. Perruquetti, T. Floquet, E. Moulay. Finite-Time Observers: Application to SecureCommunication. IEEE Trans. Automat. Control.2008,53:356~360
[71] H. Wang, Z.Z. Han, Q. Y. Xie, W. Zhang. Finite-Time Chaos Synchronization of UnifiedChaotic System with Uncertain Parameters. Commun Nonlinear Sci Numer Simulat.2009,14:2239~2247
[72] W. Yu. Finite-Time Stabilization of Three-Dimensional Chaotic Systems Based on CLF. Phys.Lett. A.2010,374:3021~3024
[73] H. Wang, Z. Han, Qi. Xie, W. Zhang. Sliding Mode Control for Chaotic Systems Based onLMI. Commun. Nonlinear Sci Numer. Simulat.2009,14:1410~1417
[74] W. Xiang, Y. Huangpu. Second-Order Terminal Sliding Mode Controller for a Class of ChaoticSystems with Unmatched Uncertainties. Commun. Nonlinear Sci. Numer. Simulat.2010,15:3241~3247
[75] H. Wang, Z. Han, Q. Xie, W. Zhang. Finite-Time Chaos Control via Nonsingular TerminalSliding Mode Control. Commun. Nonlinear Sci. Numer. Simulat.2009,14:2728~2733
[76] S. Li, Y. Tian. Finite-Time Synchronization of Chaotic Systems. Chaos Soliton Fract.2003,15:303~310
[77] H. Wang, Z. Han, Q. Xie, W. Zhang. Finite-Time Synchronization of Uncertain UnifiedChaotic Systems Based on CLF. Nonlinear Anal. RWA.2009,15:2842~2849
[78] H. Wang, Z. Han, Q. Xie, W. Zhang, Finite-Time Chaos Synchronization of Unified ChaoticSystem with Uncertain Parameters. Commun. Nonlinear Sci. Numer. Simulat.2009,14:2239~2247
[79] T. Gonzalez, J. A. Moreno, L. Fridman. Variable Gain Super-Twisting Sliding Mode Control.IEEE Trans. Automatic Control.2012,57:2100~2105
[80] T. Gonzalez, J. A. Moreno, L. Fridman,“Variable Gain Super-Twisting Sliding ModeControl,” IEEE Trans. Automatic Control,2012,57(8):2100~2105
[81] S. Z. Sarpturk, Y. Istefanopulos, O. Kaynak. On The Stability of Discrete-Time Sliding ModeControl Systems. IEEE Trans. Automatic Control,1987,32:930~932
[82] C. C. Cheng, M. H Lin, J. M. Hsiao. Sliding Mode Controllers Design for Linear Discrete-TimeSystems with Matching Perturbations. Automatica,2000,36:1205~1211
[83] J. A. Moreno, M. Osorio. Strict Lyapunov Functions for the Super-Twisting Algorithm. IEEETrans. Automatic Control.2012,57:1035~1040
[84] Q. L. Han. Improved Stability Criteria and Controller Design for Linear Neutral Systems.Automatica.2009,45:1948~1952
[85] N. Luo, D. L. M. Sen. State Feedback Sliding-Mode Control of a Class of UncertainTime-Delay Systems. IEE Proc. Control Theory Appl.1993,140:261~274
[86] M.S.Yang, P. L. Liu, H.C. Lu, Output Feedback Stabilization of Uncertain Dynamic SystemsWith Multiple State Delays via Sliding-Mode Control Strategy. Proc. IEEE Int. Symp. onIndustrial Electronics (ISIE) Conf. Bled. Slovenia.1999:1147~1152
[87] J. Hu, J. Chu, H. Su. SMVSC for a Class of Time-Delay Uncertain Systems with MismatchingUncertainties. IEE Proc., Control Theory Appl.2000,147:687~693
[88] D. Zhang, L. Yu. Exponential Stability Analysis for Neutral Switched Systems with IntervalTime-Varying Mixed Delays and Nonlinear Perturbations, Nonlinear Analysis: HybridSystems,2012,6:775~786
[89] F. Qiu, B.T. Cui, Y. Ji. Further Results On Robust Stability of Neutral System with MixedTime-Varying Delays and Nonlinear Perturbations, Nonlinear Analysis: Real WorldApplications,2010,11:895~906
[90] R. Sakthivel, K. Mathiyalagan S. Marshal Anthoni. Robust Stability and Control for UncertainNeutral Time Delay Systems. International Journal of Control.2012,85:373~383
[91] H.Y. Shao. Improved Delay-Dependent Stability Criteria for Systems with a Delay Varying ina Range. Automatica.2008,44:3215~3218
[92] K Moezzi, A. G. Aghdam. Adaptive Robust Control of Uncertain Neutral Time-Delay Systems.American Control Conference, Seattle, WA,2008:5162~5167.
[93] W.A Zhang, L.Yu. Delay-Dependent Guaranteed Cost Control for Uncertain Neutral Systemswith Nonlinear Parameter Perturbations. IET Control Theory Applications,2007,1:675~681.
[94] U. Baser, B. Kizilsac. Dynamic Output Feedback H Infinite Control Problem for Linear NeutralSystems. IEEE Transactions on Automatic Control2007,52:1113~1118
[95] Y.C. Lin, C.L. Lin. Optimal Control Approach for Robust Control Design of Neutral Systems.Optimal Control Applications&Methods,2009,30:87~102.
[96] M.V. Basin, L.M. Fridman, G. J. G. Rodriguez, P. Acosta. Optimal and Robust Sliding ModeControl for Linear Systems with Multiple Time Delays in Control Input. Asian Journal OfControl2003,5:557~567
[97] L.G. Wua, C.H. Wang, Q.S. Zeng, Observer-Based Sliding Mode Control for a Class ofUncertain Nonlinear Neutral Delay Systems Journal Of The Franklin Institute,2008(345):233~253
[98] Y. Niu, J. Lam, X. Wang. Sliding-Mode Control for Uncertain Neutral Delay Systems. IEEProc. Control Theory Appl.2004,151:38~44
[99] S. C. Qu, Z. Q. Lei, Q. M. Zhu, H. Nouri. Stabilization for a Class of Uncertain Multi-TimeDelays System Using Sliding Mode Controller. International Journal Of Innovative Computing,Information And Control.2011,7:4195~4205
[100] Y. G. He, L. Zhao, M.Y. Zhang. Advanced in Control Engineeringand Information ScienceSliding Mode Control for a class of Uncertain Neutral Delay Systems. Procedia Engineering.2011,15:1181~1185
[101] L.O.Chua, L.Yang. Cellular Neural Networks: Theory, IEEE Trans. Circuits Syst.1988,35:1257~1272
[102] J. D. Gao, J. Wang. Global Asymptotic and Robust Stability of Recurrent Neural Networkswith Delays. Circuits and Systems I.2005,52:417~426
[103] V. Singh. Improved Global Robust Stability of Interval Delayed Neural Networks via SplitInterval: Generalizations. Applied Mathematics and Computation.2008,20:290~297
[104] H. Gao, T. Chen. New Results on Stability of Discrete-Time Systems with Time-Varying StateDelay. IEEE Transactions on Automatic Control.2007,52:328~334
[105] W. D. Chang, R. C. Hwang, J. G. Hsieh, Application of an Auto-Tuning Neuron to SlidingMode Control, IEEE Transactions on Systems, Man And Cybernetics-Part C:Aplications AndRevises,2002,32(4):517:522
[106] T. C. Kuo, Y. J. Huang, S. H. Chang. Sliding Mode Control with Self-Tuning Law forUncertain Nonlinear System. ISA Transactions,2008,47:171~178
[107] C. C. Hua, S. X. Ding, X.P. Guan. Robust Controller Design for Uncertain Multiple-DelaySystems with Unknown Actuator Parameters. Automatica,2011,48:211~218
[108] D. J. Rubio, W. Yu. Nonlinear System Identification with Recurrent Neural Networks andDead-Zone Kalman Filter Algorithm. Neurocomputing.2007,70:2460~2466.
[109] I. Salgado, I. Chairez. Nonlinear Discrete Time Neural Network Observer. Neurocomputing,2013,101:73~81
[110] D. J. Rubio, W. Yu. Stability Analysis of Nonlinear System Identification via Delayed NeuralNetworks. IEEE Transactions On Circuits And Systems II: Express Briefs,2007,54:161~165
[111] S. S. Ge, F. Hong, T.H. Lee. Robust Adaptive Control of Nonlinear Systems with UnknownTime Delays. Automatica.2005,41:1181~1190
[112] S. S. Ge, G. Li, T. Lee. Adaptive NN Control for a Class of Strict-Feedback Discrete-TimeNonlinear Systems. Automatica.2003,39:807~819
[113] D. Wang, J. Huang. Adaptive Neural Network Control for a Class of Uncertain NonlinearSystems in Pure-Feedback Form. Automatica.2002,38:1365~1372
[114] G. Bartolini, E. Punta. Sliding Mode Output-Feedback Stabilization of Uncertain NonlinearNonaffine Systems. Automatica.2012,48:3106~3113
[115] T. Zhang, S. Ge, C. Hang. Design and Performance Analysis of a Direct Adaptive Controllerfor Nonlinear Systems. Automatica.1999,35:1809~1817
[116] T. Zhang, S. Ge. Adaptive Neural Control of MIMO Nonlinear State Time-Varying DelaySystems with Unknown Dead-Zones and Gain Signs. Automatica.2007,43:1021~1033
[117] N. Noroozi, M. Roopaei, M. Z. Jahromi. Adaptive Fuzzy Sliding Mode Control Scheme forUncertain Systems. Communications in Nonlinear Science and Numerical Simulation.2009,14:3978~3992
[118] W.Yu. Nonlinear System Identification Using Discrete-Time Recurrent Neural Networks withStable Learning Algorithms. Information Sciences.2004,158:131~147
[119] C. Yang, S.S. Ge, T.H. Lee. Output Feedback Adaptive Control of a Class of NonlinearDiscrete-Time Systems with Unknown Control Directions. Automatica.2009,45:270~276
[120] U. Romero. Neural Network Design and Model Reduction Approach for Black Box NonlinearSystem Identification with Reduced Number of Parameters. Neurocomputing.2013,101:170~180
[121] K. P. Tee, S. S. Ge, E. H. Tay. Barrier Lyapunov Functions for the Control ofOutput-Constrained Nonlinear Systems. Automatica.2009,45:918~927
[122] S.S.Ge, C. Wang. Direct Adaptive NN Control of a Class of Nonlinear Systems. IEEETransactions on Neural Networks.2002,13:214~221
[123] X. L. Wu, J. H. Zhang, Q. M. Zhu. A Generalized Procedure in Designing Recurrent NeuralNetwork Identification and Control of Time-Varying-Delayed Nonlinear Dynamic Systems.Neurocomputing.2010,73:1376~1383
[124] F. L. Lewis, A. Yesildirek, K. Liu. Multilayer Neural-Net Robot Controller with GuaranteedTracking Performance. IEEE Transactions on Neural Networks,1996,7:388~399
[125] M. Wu, S. S. Ge, K. S. Han. Approximation-Based Adaptive Tracking Control ofPure-Feedback Nonlinear Systems with Multiple Unknown Time-Varying Delays. IEEETransactions On Neural Networks,2010,21(11):1804~1816
[126] W. Yu. Multiple Recurrent Neural Networks for Stable Adaptive Control. Neurocomputing,2006,70:430~444
[127] V. Utkin. Sliding Mode in Control and Optimization. Berlin: Springer-Verlag,1992
[128] G. Bartolini, A. Pisano, E. Punta, E. Usai. A Survey of Application of Second-Order SlidingMode Control to Mechanical Systems. International Journal of Control.2003,76:875~982
[129] A. Pisano, A. Davila, L. Fridman, E. Usai. Cascade Control of PM DC Drives viaSecond-Order Sliding-Mode Technique. IEEE Transactions on Industrial Electronics.2008,55:3846~3854
[130] A. Ferrara, L. Magnani. Motion Control of Rigid Robot Manipulators via First and SecondOrder Sliding Modes. Journal of Intelligent Robot Systems.2007,48:23~36
[131] C. C. Cheng, M. H. Lin, J. M. Hsiao. Sliding Mode Controllers Design for LinearDiscrete-Time Systems with Matching Perturbations. Automatica.2000,36:1205~1211
[132] N. O. Lai, C. Edwards, S. K. Spurgeon. On Output Tracking Using Dynamic Output FeedbackDiscrete-Time Sliding-Mode Controllers. IEEE Trans. Automatic Control.2007.52:1975~1981
[133] P. Ignaciuk, A. Bartoszewicz. LQ Optimal Sliding Mode Supply Policy for Periodic ReviewInventory Systems. IEEE Trans. Automatic Control.2010,55:269~274
[134] T. Yoshimura. Adaptive Discrete Sliding Mode Control for Mechanical Systems withMismatched Uncertainties. Journal of Vibration and Control.2010,16:1417~1437
[135] Y. Pan, K. Furuta. Vss Control Design for Discrete-Time System. Control-Theory AndAdvanced Technology, Part1,1994,10:669~687
[136] Q. M. Zhu, L. Z. Guo. A Pole Placement Controller for Non-Linear Dynamic Plants. Proc InstnMech Engrs Part I: J Systems and Control Engineering.2010,216:467~476
[137] C. J. Taylor, A. Chotai, P.C. Young. Non-Linear Control by Input-Output State VariableFeedback Pole Assignment. International Journal of Control.2009,82:1029~1044
[138] O. M. Ghezawi, A. S. I. Zinober, S. A. Billings. Analysis and Design of Variable StructureSystems Using a Geometric Approach. International Journal of Control.1983,38:657~671
[139] K. Gu, V.L. Kharitonov, J. Chen. Stability of Time-Delay Systems, Springer-Verlag, Berlin,Germany.2003
[140] V.N. Phat. Switched Controller Design For Stabilization of Nonlinear Hybrid Systems WithTime-Varying Delays In State And Control. Journal of the Franklin Institute.2010,347:195~207
[141] T. Li, A. Song, M. Xue, H. Zhang. Stability Analysis On Delayed Neural Networks Based OnAn Improved Delay-Partitioning Approach. Journal of Computational and AppliedMathematics.2011,235:3086~3095
[142] M. Wu, Y. He, J. She, G. Liu. Delay-Dependent Criteria for Robust Stability of Time-VaryingDelay Systems. Automatica.2004,40:1435~1439
[143] Y. He, M. Wu, G. Liu, J. She. Output Feedback Stabilization for A Discrete-Time System WithA Time-Varying Delay. IEEE Transactions on Automatic Control.2008,53:2372~2377
[144] P. Shi, M.S. Mahmoud, J. Yi, A. Ismail. Worst Case Control of Uncertain Jumping Systemswith Multi-State and Input Delay Information. Information Sciences.2006,176:186~200
[145] Y. Xia, Z. Zhu, C. Li, H. Yang, Q. Zhu. Robust Adaptive Sliding Mode Control For UncertainDiscrete-Time Systems With Time Delay. Journal of the Franklin Institute.2010,347:339~357
[146] F. Gouaisbaut, D. Peaucelle. Delay-Dependent Stability Analysis Of Linear Time DelaySystems, In: IFAC Workshop On Time Delay System, L’Aquila, Italy, January2006
[147] Z. Feng, J. Lam, H. Gao, B. Du. Improved Stability and Stabilization Results for DiscreteSingular Delay Systems via Delay Partitioning, In: IEEE Conference on Decision and Controland28th Chinese Control Conference, Shanghai, China,2009
[148] G. Zhai, I. Matsune, J. Imae, T. Kobayashi. A Note on Multiple Lyapunov Functions andStability Condition for Switched and Hybrid Systems. International Journal of InnovativeComputing, Information and Control.2009,5:1189~1199
[149] R. Wang, J. Zhao. Exponential Stability Analysis for Discrete-Time Switched Linear Systemswith Time-Delay. Information and Control.2007,3:1557~1564
[150] L. Wu, Z. Wang. Guaranteed Cost Control For Linear Switched Systems With Neutral Delayvia Dynamic Output Feedback. International Journal of Systems Science.2009,40:717~728
[151] W. Xiang, J. Xiao. H Infinite Finite-Time Control for Switched Nonlinear Discrete-TimeSystems with Norm-Bounded Disturbance. Journal of the Franklin Institute.2011,348:331~352
[152] W. Zhang, L. Yu, S. Yin. A Switched System Approach to H Infinite Control of NetworkedControl Systems with Time-Varying Delays. Journal of the Franklin Institute.2011,348:165~178
[153] L. Wu, J. Lam. Sliding Mode Control of Switched Hybrid Systems With Time-Varying Delay.International Journal of Adaptive Control and Signal Processing.2008,22:909~931
[154] M. Basin, A. Ferreira, L.M. Fridman. Sliding Mode Identification and Control For LinearUncertain Stochastic Systems. International Journal of Systems Science.2007,38:861~869
[155] S. Vaidyanathan. Hybrid Chaos Synchronization of Hyperchaotic Newton-Leipnik Systems bySliding Mode Control. International Journal of Control Theory and Computer Modelling.2011,1:1~10
[156] Y. Xia, Y. Jia. Robust Sliding-Mode Control For Uncertain Time-Delay Systems: An LMIApproach. IEEE Transactions on Automatic Control.2003,48:1086~1092
[157] Y. Niu, J. Lam, X. Wang. Sliding-Mode Control for Uncertain Neutral Delay Systems. IEEProceedings: Part D. Control Theory and Applications.2004,151:38~44
[158] X. X. Yu, C. F. Wu, F. Z. Liu. Sliding Mode Control of Discrete-Time Switched Systems withTime-Delay. Journal of the Franklin Institute.2013,350:19~33