Robust delayed-state-feedback stabilization of uncertain stochastic systems

Due to time spent in computation and transfer, control input is usually subject to delays. Problems of deterministic systems with input delay have received considerable attention. However, relatively few works are concerned with problems of stochastic system with input delay. This paper studies delayed-feedback stabilization of uncertain stochastic systems. Based on a new delay-dependent stability criterion established in this paper, a robust delayed-state-feedback controller that exponentially stabilizes the uncertain stochastic systems is proposed. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method.

[1]  X. Mao,et al.  Exponential stability of stochastic delay interval systems , 2000 .

[2]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[3]  Feiqi Deng,et al.  Robust Exponential Stabilization of Stochastic Large-scale Delay Systems , 2007, 2007 IEEE International Conference on Control and Automation.

[4]  Wook Hyun Kwon,et al.  Robust stabilization of uncertain input-delayed systems using reduction method , 2001, Autom..

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

[6]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[7]  Young Soo Moon,et al.  Delay-dependent robust stabilization of uncertain state-delayed systems , 2001 .

[8]  Ren C. Luo,et al.  Stabilization for linear uncertain system with time latency , 2002, IEEE Trans. Ind. Electron..

[9]  Wei Xing Zheng,et al.  On improved robust stabilization of uncertain systems with unknown input delay , 2006, Autom..

[10]  Chong Lin,et al.  Delay‐dependent robust stability for stochastic time‐delay systems with polytopic uncertainties , 2008 .

[11]  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.

[12]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[13]  X. Mao,et al.  Robustness of exponential stability of stochastic differential delay equations , 1996, IEEE Trans. Autom. Control..

[14]  Qing-Guo Wang,et al.  Delay-range-dependent stability for systems with time-varying delay , 2007, Autom..

[15]  A. Rodkina,et al.  On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays , 2008 .

[16]  Michael V. Basin,et al.  On delay-dependent stability for a class of nonlinear stochastic delay-differential equations , 2006, Math. Control. Signals Syst..

[17]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[18]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[19]  Bugong Xu,et al.  Stability robustness bounds for linear systems with multiple time-varying delayed perturbations , 1997, Int. J. Syst. Sci..

[20]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[21]  X. Mao,et al.  Robust stability of uncertain stochastic differential delay equations , 1998 .

[22]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[23]  Zhi-Hong Guan,et al.  Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach , 2005, Syst. Control. Lett..

[24]  X. Mao,et al.  Razumikhin-type theorems on exponential stability of stochastic functional differential equations , 1996 .

[25]  Dong Yue,et al.  Delayed feedback control of uncertain systems with time-varying input delay , 2005, Autom..

[26]  Xuerong Mao,et al.  The improved LaSalle-type theorems for stochastic functional differential equations , 2006 .

[27]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[28]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[29]  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).

[30]  Dong-Sung Kim,et al.  Maximum allowable delay bounds of networked control systems , 2003 .

[31]  Dong Yue,et al.  Robust stabilization of uncertain systems with unknown input delay , 2004, Autom..

[32]  Shengyuan Xu,et al.  Robust stochastic stabilization and H∞ control of uncertain neutral stochastic time-delay systems☆ , 2006 .

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