Design of Estimator-Based Sliding-Mode Output-Feedback Controllers for Discrete-Time Systems

This paper considers the output-feedback sliding-mode-control (SMC) problem for a class of discrete-time systems with matched disturbances. A novel approach to the design of the sliding surface is proposed, which is based on a novel result on discrete-time singular systems. For the state variables which cannot be obtained from output variables directly, a simple estimator is proposed to estimate them. Then, the estimator-based robust SMC law is also proposed by using a new reaching law. It is further shown that the closed-loop control system is uniformly ultimately bounded. Furthermore, a memory-based sliding-mode controller with a modified estimator is also proposed. Finally, numerical examples are given to illustrate the effectiveness of the proposed design methods.