Nonfragile $H_{\infty}$ Filter Design for T–S Fuzzy Systems in Standard Form

Abstract

This paper is concerned with the problem of nonfragile H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for continuous-time Takagi-Sugeno (T-S) fuzzy systems. The filter to be designed is assumed to have two types of multiplicative gain variations. First, two relaxed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering analysis conditions are proposed based on useful linear matrix inequality preliminaries. Whereafter, the results are exploited to derive sufficient conditions for designing a nonfragile H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter, which guarantees a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance of the filtering error system. Compared with the existing results, the proposed design methods not only suit for a standard form of the fuzzy filter but also give more relaxed design conditions. Finally, simulation examples will be given to show the efficiency of the proposed design methods.