Sliding mode exponential H∞ synchronization of Markovian jumping master-slave systems with time-delays and nonlinear uncertainties

This paper investigates the problem of exponential H∞ synchronization for a class of master-slave systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H∞ synchronization of the two coupled master and slave systems regardless of their initial states. A numerical example is given to show the effectiveness of the method.

[1]  J. Lam,et al.  Stochastic stabilizability and H∞ control for discrete-time jump linear systems with time delay ☆ , 1999 .

[2]  E. Boukas,et al.  H∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty , 1997 .

[3]  Qing-Guo Wang,et al.  Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays , 2006 .

[4]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[5]  Andreas Antoniou,et al.  A near-optimal multiuser detector for DS-CDMA systems using semidefinite programming relaxation , 2003, IEEE Trans. Signal Process..

[6]  Abdellah Benzaouia,et al.  Stability of discrete-time linear systems with Markovian jumping parameters and constrained control , 2002, IEEE Trans. Autom. Control..

[7]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[8]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  Shengyuan Xu,et al.  Robust H∞ filtering for uncertain Markovian jump systems with mode-dependent time delays , 2003, IEEE Trans. Autom. Control..

[10]  Weidong Zhang,et al.  Sliding Mode Control of Uncertain Neutral Stochastic Systems with Multiple Delays , 2008 .

[11]  Yuanqing Xia,et al.  Robust sliding-mode control for uncertain time-delay systems: an LMI approach , 2003, IEEE Trans. Autom. Control..

[12]  James Lam,et al.  Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  A. I. Matasov,et al.  Neutral Stochastic Differential Delay Equations with Markovian Switching , 2003 .

[14]  Ju H. Park.  Synchronization of Genesio chaotic system via backstepping approach , 2006 .

[15]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[16]  Ricardo Femat,et al.  Adaptive synchronization of high-order chaotic systems: a feedback with low-order parametrization , 2000 .

[17]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[18]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[19]  Daniel W. C. Ho,et al.  Sliding mode control of singular stochastic hybrid systems , 2010, Autom..

[20]  Jinde Cao,et al.  Global robust point dissipativity of interval neural networks with mixed time-varying delays , 2009 .

[21]  Jiang-Wen Xiao,et al.  Adaptive control and synchronization for a class of nonlinear chaotic systems using partial system states , 2006 .

[22]  Yuanqing Xia,et al.  On designing of sliding-mode control for stochastic jump systems , 2006, IEEE Transactions on Automatic Control.

[23]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Hamid Reza Karimi,et al.  Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks , 2009 .

[25]  Xingyu Wang,et al.  Sliding mode control for Itô stochastic systems with Markovian switching , 2007, Autom..

[26]  Teh-Lu Liao,et al.  Adaptive synchronization of chaotic systems and its application to secure communications , 2000 .