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.