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

In this paper, the design of sliding mode control is addressed for uncertain stochastic systems modeled by Itô differential 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 H∞ technique such that the robustly stochastic stability with a prescribed disturbance attenuation level γ can be obtained. A sufficient condition for the existence of the desired sliding mode controller is obtained via linear matrix inequalities (LMIs). The reachability of the specified sliding surface is proven. Finally, a numerical simulation is presented to illustrate the proposed method. Copyright c © 2002 John Wiley & Sons, Ltd.