L 2-Gain Control for T-S Fuzzy Systems Over an Event-Triggered Communication Network Using Delay Decomposition and Deviation Bounds of Membership Functions

Abstract

This paper is concerned with networked \(L_2\)-gain control for a T-S fuzzy system over an event-triggered communication network. Taking an event-triggered communication scheme and network-induced delays into consideration, the networked control system is described by an asynchronous T-S fuzzy system with an interval time-varying delay. Due to variation characteristic of network-induced delays, the interval is decomposed into N subintervals and the jumping among these subintervals is governed by a Markov chain. A new relaxation method, which fully utilizes the convexity of normalized membership functions and the deviation bounds of asynchronous normalized membership functions, is proposed and a stochastic Lyapunov–Krasovskii functional is constructed to derive some delay-dependent criteria on \(L_2\)-gain performance analysis and controller design of the asynchronous T-S fuzzy system. An illustrative example is provided to show that the proposed criteria are of less conservatism and less computational complexity than some existing results, and are effective in achieving a prescribed \(L_2\)-gain performance.