H∞ Filter for Discrete-Time Takagi–Sugeno Fuzzy Systems with Time-Varying Delays via a Novel Wirtinger-Based Inequality

Abstract

This paper is devoted to the analysis and design of H∞ filtering for discrete-time Takagi–Sugeno (TS) fuzzy systems with time-varying delays. By using the delay-partitioning method, more systematic information is introduced, which can reduce the conservatism of the conclusion. By constructing an appropriate Lyapunov functional and combining with a newly Wirtinger-based summation inequality, the existence condition of the H∞ filter is obtained. Thus, utilizing the contract matrix transformation method, the H∞ filter design for discrete-time TS fuzzy systems with time-varying delay based on LMI is proposed. Finally, a few numerical analysis results are given to prove the effectiveness of the method.