An Output Feedback Control Design for {\rm H}_\infty Synchronization of Master-Slave Markovian Jump Systems with Time-Varying Delays

In this chapter, an output feedback control proach is proposed for exponential synchronization problem of master slave systems with both discrete and distributed time-varying delays 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 mode-dependent output feedback control law in terms of linear matrix inequalities. The controller guarantees the \( {\rm{H}}_\infty \) 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]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

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

[3]  Harris Wu,et al.  Robust sliding mode control for uncertain linear discrete systems independent of time-delay , 2011 .

[4]  Xiaohua Xia,et al.  Identifiability of nonlinear systems with application to HIV/AIDS models , 2003, IEEE Trans. Autom. Control..

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

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

[7]  Magdi S. Mahmoud,et al.  Robust stability, stabilization and H-infinity control of time-delay systems with Markovian jump parameters , 2003 .

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

[9]  M. Mahmoud,et al.  Robust Kalman filtering for continuous time-lag systems with Markovian jump parameters , 2003 .

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

[11]  Yugang Niu,et al.  Stabilization of discrete-time stochastic systems via sliding mode technique , 2012, J. Frankl. Inst..

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

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

[14]  Hamid Reza Karimi,et al.  A linear matrix inequality approach to robust fault detection filter design of linear systems with mixed time-varying delays and nonlinear perturbations , 2010, J. Frankl. Inst..

[15]  Magdi S. Mahmoud,et al.  $H_\infty$ and robust control of interconnected systems with Markovian jump parameters , 2005 .

[16]  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).

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

[18]  James Lam,et al.  Nonlinear filtering for state delayed systems with Markovian switching , 2003, IEEE Trans. Signal Process..

[19]  Lixian Zhang,et al.  H∞ estimation for discrete-time piecewise homogeneous Markov jump linear systems , 2009, Autom..

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

[21]  M. Mahmoud,et al.  Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities , 2002 .

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

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

[24]  Lixian Zhang,et al.  Mode-dependent Hinfinity filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

[25]  Huijun Gao,et al.  State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems , 2010, IEEE Transactions on Automatic Control.

[26]  Yuanqing Xia,et al.  Observer-based sliding mode control for a class of discrete systems via delta operator approach , 2010, J. Frankl. Inst..

[27]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

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

[29]  James Lam,et al.  Necessary and Sufficient Conditions for Analysis and Synthesis of Markov Jump Linear Systems With Incomplete Transition Descriptions , 2010, IEEE Transactions on Automatic Control.

[30]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[31]  Lixian Zhang,et al.  Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities , 2009, Autom..

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

[33]  Yan Shi,et al.  Output feedback stabilization and disturbance attenuation of time-delay jumping systems , 2003, IMA J. Math. Control. Inf..

[34]  El-Kébir Boukas,et al.  Robust production and maintenance planning in stochastic manufacturing systems , 1995, IEEE Trans. Autom. Control..

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

[36]  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.

[37]  Dragoslav D. Siljak,et al.  Design of robust static output feedback for large-scale systems , 2004, IEEE Transactions on Automatic Control.

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

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

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

[41]  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.

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

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

[44]  Hamid Reza Karimi,et al.  Observer-Based Mixed H2/H∞ Control Design for Linear Systems with Time-Varying Delays: An LMI Approach , 2008 .