Stability Analysis and Robust H ∞ Control of Switched Stochastic Systems with Time-Varying Delay

Abstract

The problems of mean-square exponential stability and robust $H_{\infty }$ control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then, $H_{\infty }$ performance is studied and robust $H_{\infty }$ controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.