Discrete-time sliding mode control for networked systems with random communication delays

This paper aims to design a robust discrete-time sliding mode control (DSMC) for the uncertain discrete-time networked systems involving time-varying Communication delays. To this end, the so-called Bernoulli random binary distribution is utilized to model the random time-varying delays. Then, by exploiting a specific sliding surface, a discrete-time sliding mode controller is designed such that the derived closed-loop system state and sliding function remain bounded in the presence of uncertainties and exogenous disturbances. Since the system state and sliding function are involved time-varying delays, the notion of exponentially mean square stability will be used to guarantee the stability/boundedness of the derived closed-loop system. The proposed robust DSMC can also overcome the conservatism of the existing methods in the literature. An illustrative example is presented to show the effectiveness of the proposed approach.