Robust sliding mode design for uncertain stochastic systems based on H∞ control method

SUMMARY In this paper, the design of sliding mode control is addressed for uncertain stochastic systems modeled by It^o difierential equations. There exist the parameter uncertainties in both the state and input matrices, and the unmatched external disturbance. The key feature of this work is the integration of sliding mode control method with H1 technique such that the robustly stochastic stability with a prescribed disturbance attenuation level ∞ can be obtained. A su‐cient condition for the existence of the desired sliding mode controller is obtained via linear matrix inequalities (LMIs). The reachability of the specifled sliding surface is proven. Finally, a numerical simulation is presented to illustrate the proposed method. Copyright c ∞ 2002 John Wiley & Sons, Ltd.

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

[2]  Hong-ke Wang,et al.  On the Exponential Stability of Stochastic Differential Equations , 2009, ICFIE.

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

[4]  J. Geromel,et al.  Numerical comparison of output feedback design methods , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Weihai Zhang,et al.  State Feedback HINFINITY Control for a Class of Nonlinear Stochastic Systems , 2006, SIAM J. Control. Optim..

[6]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1997, IEEE Trans. Autom. Control..

[7]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[8]  R. Skelton,et al.  The XY-centring algorithm for the dual LMI problem: a new approach to fixed-order control design , 1995 .

[9]  Daniel W. C. Ho,et al.  A note on the robust stability of uncertain stochastic fuzzy systems with time-delays , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[10]  K. Grigoriadis.  Optimal H ∞ model reduction via linear matrix inequalities: continuous- and discrete-time cases , 1995 .

[11]  Daniel W. C. Ho,et al.  Robust observer design for Itô stochastic time-delay systems via sliding mode control , 2006, Syst. Control. Lett..

[12]  R. Skelton,et al.  LMI numerical solution for output feedback stabilization , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[13]  W. Wonham.  On a Matrix Riccati Equation of Stochastic Control , 1968 .

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

[15]  James Lam,et al.  Robust integral sliding mode control for uncertain stochastic systems with time-varying delay , 2005, Autom..

[16]  Wen-Jun Cao,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Trans. Autom. Control..

[17]  H. Choi.  Variable structure control of dynamical systems with mismatched norm-bounded uncertainties: An LMI approach , 2001 .

[18]  Bill Diong,et al.  Sliding-mode control design for a class of systems with non-matching nonlinearities and disturbances , 2004 .

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