Delay-Dependent Robust Stabilization and H∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays

This paper considers the problems of delay-dependent robust stabilization and H∞ control for nonlinear stochastic systems with Markovian jump parameters and interval time-varying delays. Based on the Lyapunov method and introducing some appropriate free-weighting matrices, sufficient conditions for the solvability of above problems have been investigated in terms of linear matrix inequalities (LMIs). Furthermore, the desired state feedback controller has also been designed by solving these LMIs. Finally, a numerical example is provided to demonstrate the potential of the proposed techniques.

[1]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[2]  Emilia Fridman,et al.  A descriptor system approach to H∞ control of linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[3]  Hanyong Shao.  Delay-range-dependent robust H∞ filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters , 2008 .

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[6]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[7]  V. Kolmanovskii,et al.  Applied Theory of Functional Differential Equations , 1992 .

[8]  Guoliang Wei,et al.  Nonlinear H∞ control of stochastic time-delay systems with Markovian switching , 2008 .

[9]  X. Xu,et al.  Impulsive control in continuous and discrete-continuous systems [Book Reviews] , 2003, IEEE Transactions on Automatic Control.

[10]  Keith J. Burnham,et al.  On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters , 2002, IEEE Trans. Autom. Control..

[11]  Xiaohui Liu,et al.  Stabilization of a class of stochastic nonlinear time-delay systems , 2004 .

[12]  Junwei Lu,et al.  Robust H∞ Control for Stochastic Time-Delay Systems with Markovian Jump Parameters via Parameter-Dependent Lyapunov Functionals , 2008 .

[13]  J. Lam,et al.  Delay-dependent robust H∞ control for uncertain systems with time-varying delays , 1998 .

[14]  E. Boukas,et al.  H∞-Control for Linear Time-Delay Systems with Markovian Jumping Parameters , 2000 .

[15]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[16]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[17]  Shengyuan Xu,et al.  Technical communique: New results on delay-dependent robust H∞ control for systems with time-varying delays , 2006 .

[18]  Bing Chen,et al.  A Delay-Dependent Approach to Robust H∞ Control for Uncertain Stochastic Systems with State and Input Delays , 2009, Circuits Syst. Signal Process..

[19]  Ju H. Park.  Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties , 2001 .

[20]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[21]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[22]  Shengyuan Xu,et al.  Robust reliable H-infinity control for nonlinear uncertain stochastic time-delay systems with Markovian jumping parameters , 2008 .

[23]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[24]  P. Pardalos,et al.  Optimization and Control of Bilinear Systems: Theory, Algorithms, and Applications , 2008 .

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

[26]  Ju H. Park,et al.  Matrix Inequality Approach to a Novel Stability Criterion for Time-Delay Systems with Nonlinear Uncertainties , 2005 .

[27]  Vu Ngoc Phat,et al.  Robust Stabilization of Linear Systems with Delayed State and Control , 2009 .

[28]  El-Kebir Boukas,et al.  Deterministic and Stochastic Time-Delay Systems , 2002 .

[29]  Zidong Wang,et al.  Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities , 2001 .

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

[31]  M Pardalos Panos,et al.  Optimization and Control of Bilinear Systems , 2008 .

[32]  Huijun Gao,et al.  Robust H∞ Filtering for Uncertain Discrete Stochastic Systems with Time Delays , 2005 .

[33]  Zidong Wang,et al.  Robust H∞ control of stochastic time‐delay jumping systems with nonlinear disturbances , 2006 .

[34]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[35]  H. Chizeck,et al.  Controllability, observability and discrete-time markovian jump linear quadratic control , 1988 .

[36]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[37]  R. P. Marques,et al.  Robust H 2-control for discrete-time Markovian jump linear systems , 2000 .

[38]  Shengyuan Xu,et al.  Delay-Dependent $H_{\infty }$ Control and Filtering for Uncertain Markovian Jump Systems With Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[39]  Shengyuan Xu,et al.  Robust H∞ control for uncertain stochastic systems with state delay , 2002, IEEE Trans. Autom. Control..

[40]  Dong Yue,et al.  Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching , 2005, IEEE Transactions on Automatic Control.

[41]  Hong-Kun Xu.  Strong convergence of an iterative method for nonexpansive and accretive operators , 2006 .

[42]  Zhang Hong-qiang.  Robust Stochastic Stabilization and H_∞ Control of Uncertain Neutral Stochastic Time-Delay Systems , 2008 .

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

[44]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[45]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..