Reliable H∞ control for discrete-time stochastic systems with mixed time-varying delays

In this paper, the reliable H∞ control problem for a class of discrete-time stochastic delay system (DTSDS) is investigated. The system under consideration includes Itô-type stochastic disturbance and mixed time-varying delay including discrete-time delay and continuous-time delays. Our aim is to design a controller such that, for possible actuator failures, the closed-loop DTSDS is mean-square asymptotically stable with disturbance attenuation γ. Based on the Lyapunov stability theory and Itô differential rule, together with linear matrix inequality(LMI), the sufficient conditions of the solvability of the reliable H∞ controller for DTSDS are given. Finally, A numerical example is exploited to show the usefulness of the derived results and the effectiveness of the proposed methods.