Reliable stabilization of stochastic time-delay systems with nonlinear disturbances

This paper is concerned with the stabilization problem for a class of continuous stochastic time-delay systems with nonlinear disturbances, parameter uncertainties and possible actuator failures. Both the stability analysis and synthesis problems are considered. The purpose of the stability analysis problem is to derive easy-to-test conditions for the uncertain nonlinear time-delay systems to be stochastically, exponentially stable. The synthesis problem, on the other hand, aims to design state feedback controllers such that the closed-loop system is exponentially stable in the mean square for all admissible uncertainties, nonlinearities, time-delays and possible actuator failures. It is shown that the addressed problem can be solved in terms of the positive definite solutions to certain algebraic matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed design method.

[1]  P. Sannuti,et al.  Observer-Based Control of Uncertain Systems with Nonlinear Uncertainties , 1989, 1989 American Control Conference.

[2]  Keith J. Burnham,et al.  Robust filtering for a class of stochastic uncertain nonlinear time-delay systems via exponential state estimation , 2001, IEEE Trans. Signal Process..

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

[4]  Edwin Engin Yaz,et al.  On LMI formulations of some problems arising in nonlinear stochastic system analysis , 1999, IEEE Trans. Autom. Control..

[5]  Yuli Fu,et al.  BIBO stabilization of stochastic delay systems with uncertainty , 2003, IEEE Trans. Autom. Control..

[6]  Yungang Liu,et al.  Output feedback control design for strict-feedback stochastic nonlinear systems under a risk-sensitive cost , 2003, IEEE Trans. Autom. Control..

[7]  Lihua Xie,et al.  Robust Kalman filtering for uncertain systems , 1994 .

[8]  Uwe Mackenroth,et al.  H 2 Optimal Control , 2004 .

[9]  Hong Qiao,et al.  Robust filtering for bilinear uncertain stochastic discrete-time systems , 2002, IEEE Trans. Signal Process..

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

[11]  E. Boukas,et al.  On Stochastic Stabilization of Discrete‐Time Markovian Jump Systems with Delay in State , 2003 .

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

[13]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

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

[15]  Lihua Xie,et al.  Decentralized stabilization of a class of interconnected stochastic nonlinear systems , 2000, IEEE Trans. Autom. Control..

[16]  Byung Kook Kim,et al.  Robust and reliable H∞ control for linear systems with parameter uncertainty and actuator failure , 1996, Autom..

[17]  Miroslav Krstic,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 2001, IEEE Trans. Autom. Control..

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

[19]  Heinz Unbehauen,et al.  Robust reliable control for a class of uncertain nonlinear state-delayed systems , 1999, Autom..

[20]  Charalambos D. Charalambous.  Stochastic nonlinear minimax dynamic games with noisy measurements , 2003, IEEE Trans. Autom. Control..

[21]  Ali Saberi,et al.  Observer-based control of uncertain systems with non-linear uncertainties , 1990 .

[22]  Xing-Gang Yan,et al.  Output feedback sliding mode control for nonminimum phase systems with nonlinear disturbances , 2004, 2004 5th Asian Control Conference (IEEE Cat. No.04EX904).

[23]  Ruth J. Williams,et al.  Stabilization of stochastic nonlinear systems driven by noise of unknown covariance , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).