Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities

Abstract

This paper investigates the robust sliding mode control (SMC) problem for a class of uncertain nonlinear stochastic systems with mixed time delays. Both the sectorlike nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and randomly occurring nonlinearities obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The mixed time delays consist of both the discrete and the distributed delays. The time-varying delays are allowed in state. By employing the idea of delay fractioning and constructing a new Lyapunov–Krasovskii functional, sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface by solving a certain semidefinite programming problem. A full-state feedback SMC law is designed to guarantee the reaching condition. A simulation example is given to demonstrate the effectiveness of the proposed SMC scheme.