Quasi-sliding mode control for discrete-time uncertain systems with time-varying delay and stochastic disturbance

This paper investigates an effective controller design method for discrete-time linear system with parameter uncertainty, time-varying delay, input nonlinearity and process disturbance. A novel discrete-time quasi-sliding mode control (DQSMC) scheme is mainly proposed. Since the sliding mode bound is directly involved in the DQSMC law, the chattering bound can be accurately specified. By the proposed method, the dynamic of the sliding mode is unable to escape from the pre-given neighbourhood once it is attracted into the neighbourhood, in addition, the closed-loop system achieves the almost surely stable in mean square sense. Moreover, the proposed DQSMC provides a convenient method to simultaneously regulate the convergence rates of the sliding mode and the closed-loop system. Numerical example is provided to demonstrate the effectiveness of the proposed method.