Finite-Time Event-Triggered $\mathcal{H}_{\infty }$ Control for T–S Fuzzy Markov Jump Systems

This paper investigates the finite-time event-triggered 'I-1 control problem for Takagi-Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this paper is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closed-loop system is finite-time bounded and satisfies a prescribed 'I-1 performance level, but also the communication burden is reduced. First, a sufficient condition is established for the finite-time bounded 'I-1 performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the method of the desired controller design is presented. Two illustrative examples are finally presented to demonstrate the practicability and efficacy of the proposed method.