Sampled-Data Synchronization of Chaotic Lur'e Systems With Time Delays

This paper studies the problem of sampled-data control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems with time delays. It is assumed that the sampling periods are arbitrarily varying but bounded. In order to take full advantage of the available information about the actual sampling pattern, a novel Lyapunov functional is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Based on the Lyapunov functional, an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems. The desired sampled-data controller is designed by a linear matrix inequality approach. The effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of Chua's circuit and neural network.

[1]  David J. Hill,et al.  Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[3]  Yong He,et al.  Exponential synchronization of neural networks with time-varying mixed delays and sampled-data , 2010, Neurocomputing.

[4]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[5]  Hong-yong Yang,et al.  New globally asymptotical synchronization of chaotic Lur'e systems using sampled data , 2010, Proceedings of the 2010 American Control Conference.

[6]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[7]  Jinde Cao,et al.  Synchronization Error Estimation and Controller Design for Delayed Lur'e Systems With Parameter Mismatches , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Peng Shi,et al.  Fuzzy Hinfinity output feedback control of nonlinear systems under sampled measurements , 2003, Autom..

[9]  James Lam,et al.  Stability and Dissipativity Analysis of Static Neural Networks With Time Delay , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Meikang Qiu,et al.  ${\rm H}_{\infty}$ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[12]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[13]  Peng Shi,et al.  Exponential Synchronization of Neural Networks With Discrete and Distributed Delays Under Time-Varying Sampling , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[14]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Peng Shi,et al.  Robust sampled-data control for Markovian jump linear systems , 2006, Autom..

[16]  I. H. Mufti,et al.  Absolute stability of nonlinear control systems , 1966 .

[17]  Qing-Long Han,et al.  Fault-Tolerant Master–Slave Synchronization for Lur'e Systems Using Time-Delay Feedback Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Alexandre Seuret,et al.  A novel stability analysis of linear systems under asynchronous samplings , 2012, Autom..

[19]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  P. Shi.  Filtering on sampled-data systems with parametric uncertainty , 1998, IEEE Trans. Autom. Control..

[21]  Meiqin Liu,et al.  H∞ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model. , 2012, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[22]  James Lam,et al.  Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays , 2008, Int. J. Control.

[23]  Di Wu,et al.  STABILITY ANALYSIS FOR SAMPLED-DATA SYSTEMS BASED ON MULTIPLE LYAPUNOV FUNCTIONAL METHOD , 2012 .

[24]  Meiqin Liu,et al.  Delayed Standard Neural Network Models for Control Systems , 2007, IEEE Transactions on Neural Networks.

[25]  Yuqiang Wu,et al.  FINITE-TIME CONTROL FOR SWITCHED DELAY SYSTEMS VIA DYNAMIC OUTPUT FEEDBACK , 2012 .

[26]  Guanrong Chen,et al.  Chaos Synchronization of General Lur'e Systems via Time-Delay Feedback Control , 2003, Int. J. Bifurc. Chaos.

[27]  Wu-Hua Chen,et al.  On Sampled-Data Control for Master-Slave Synchronization of Chaotic Lur'e Systems , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[28]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

[29]  P. Shi,et al.  Fuzzy H∞ output feedback control of nonlinear systems under sampled measurements , 2001, IEEE Conference on Decision and Control.

[30]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[31]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[32]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[33]  Meikang Qiu,et al.  Exponential ${\rm H}_{\infty}$ Synchronization of General Discrete-Time Chaotic Neural Networks With or Without Time Delays , 2010, IEEE Transactions on Neural Networks.

[34]  D. Rees,et al.  STABILITY ANALYSIS FOR SYSTEMS WITH LARGE DELAY PERIOD : A SWITCHING METHOD , 2012 .

[35]  Zijiang Yang,et al.  Lag Synchronization of Unknown Chaotic Delayed Yang–Yang-Type Fuzzy Neural Networks With Noise Perturbation Based on Adaptive Control and Parameter Identification , 2009, IEEE Transactions on Neural Networks.

[36]  Xue-Jun Xie,et al.  ADAPTIVE OUTPUT FEEDBACK STABILIZATION USING MT-FILTERS FOR NONLINEAR SYSTEMS WITH INPUT AND OUTPUT TIME-DELAY , 2012 .

[37]  Qing-Long Han,et al.  On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[38]  Ikuro Mizumoto,et al.  Fast Rate Adaptive Output Feedback Control of Multirate Sampled Systems with an Adaptive Output Estimator , 2009, 2009 Fourth International Conference on Innovative Computing, Information and Control (ICICIC).

[39]  Huaguang Zhang,et al.  Novel Weighting-Delay-Based Stability Criteria for Recurrent Neural Networks With Time-Varying Delay , 2010, IEEE Transactions on Neural Networks.