Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. by utilizing a new lyapunov-krasovskii functional and some well-known inequalities,some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (lmi). then based on the state feedback controller,the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. the controller gain is designed to ensure the robust stochastic stability of the closed-loop system. finally,illustrative examples are given to demonstrate the effectiveness of the proposed method. © 2016 shuang liang and yali dong.