SMC for Discrete Fuzzy Semi-Markov Jump Models With Partly Known Semi-Markov Kernel

Abstract

This article investigates the sliding mode control (SMC) for discrete-time nonlinear semi-Markov jump models with a partly known semi-Markov kernel (SMK). The nonlinear system is characterized by the Takagi–Sugeno (T–S) fuzzy model, where the membership functions for fuzzy rules are designed to be related to the system mode. In view of the fact that the statistical characteristic of the SMK is difficult to fully obtain in practical engineering, the SMK is recognized to be partly known with less conservativeness than both semi-Markov jump models with completely known SMK and Markov jump models with partly known transition probabilities. On the basis of classical Lyapunov stability and fuzzy-model-based approach, novel convex mean-square stability is proposed for the underlying system by eliminating the nonlinear coupling terms with the aid of additional matrix variables. Afterward, a fuzzy SMC law strategy is constructed to guarantee the reachability of the discrete quasi-sliding mode. Finally, a robot arm model is simulated to verify the proposed fuzzy SMC strategy.