State Estimation and Sliding Mode Control for Non-Linear Singular Systems with Time-Varying Delay

Abstract This paper deals with the sliding mode control (SMC) problem for a class of nonlinear discrete-time singular systems with external disturbances and time-varying delay. The main contribution of this paper is to design an observer-based sliding mode control scheme for the system under consideration. First, a delay dependent criterion is built to guarantee the closed-loop system to be robustly admissible. Then, a (SMC) law is synthesized to guarantee the state trajectories of the closed-loop systems to be stable, to and ensure the reachability of the specified sliding surface in a short time interval. An illustrative example is given to numerically demonstrate the effectiveness of the proposed control scheme.