Finite‐time robust fuzzy control for non‐linear Markov jump systems under aperiodic sampling and actuator constraints

Abstract

This study investigates the fuzzy control problem for a class of non-linear Markov jump systems with sampled-data inputs and actuator constraints over a finite-time interval. Takagi–Sugeno (T–S) fuzzy models are employed to approximate the non-linearity. The partly known transition probability matrix consisting of known, uncertain, and unknown elements is considered. The asynchronous errors of the membership functions induced by aperiodic sampling are taken care of to avoid conservative results. The objective is to procure a sampled-data fuzzy controller such that the resulting closed-loop system is finite-time bounded and a prescribed performance index is guaranteed simultaneously. By establishing a new piecewise Lyapunov–Krasovskii functional and utilising convex optimisation technique, a novel set of sufficient conditions for the existence of anticipated sampled-data controller are developed. Finally, two illustrative examples are presented to prove the effectiveness of the proposed approaches.