Event-Triggered Nonsynchronized $\mathcal {H}_{\infty }$ Filtering for Discrete-Time T–S Fuzzy Systems Based on Piecewise Lyapunov Functions

Abstract

This paper is concerned with the design of ${\mathcal {H}_{\infty }}$ event-triggered filter for a class of Takagi–Sugeno fuzzy systems. Based on the proposed communication strategy, only the measured outputs of the physical plant that violate a predefined triggering condition will win the right for transmission in the shared communication channel. Considering that the implementation of the filter may not be synchronized with the plant trajectories due to the asynchronous premise variables in network environment, a novel observer-based piecewise fuzzy filter is proposed. By adopting the idea of input delay method, the filtering error dynamics is reformulated as a new event-triggered piecewise fuzzy system. By applying a piecewise Lyapunov–Krasovskii functional and some techniques on matrix convexification, a method of event-triggered ${\mathcal {H}_{\infty }}$ piecewise filter design is developed for the filtering error system concerned to be asymptotically stable with a given disturbance attenuation level and reduced transmission rate. Moreover, a co-design algorithm to derive the filter gains and the event triggering parameters is proposed. Illustrative examples are finally given to show the effectiveness of the developed method.