Robust H∞ sliding mode control for discrete time-delay systems with stochastic nonlinearities

This paper is concerned with the robust H∞ sliding mode control (SMC) problem for a general class of discrete time-delay uncertain systems with stochastic nonlinearities. The time-varying delay is unknown with given lower and upper bounds, and the stochastic nonlinearities are described by statistical means. The purpose of the problem addressed is to integrate the SMC method with the H∞ technique such that, for all admissible parameter uncertainty, unmatched stochastic nonlinearities, time-varying delay and unmatched external disturbance, the closed-loop system is asymptotically mean-square stable while achieving a prescribed disturbance attenuation level. Sufficient conditions are presented to ensure the desired performance of the system dynamics in the specified sliding surface by solving a semi-definite programming problem. Moreover, a discrete-time SMC law is synthesized to ensure the reaching condition. A simulation example is given to illustrate the validity of the proposed SMC scheme.