Robust Nonfragile $H_\infty$ Filtering of Fuzzy Systems With Linear Fractional Parametric Uncertainties

Abstract

This paper is concerned with the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Different from existing results for fuzzy <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering, the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties. Attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance, where the filter to be designed is assumed to have gain variations. By a descriptor representation approach, two sufficient conditions for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter design are proposed in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is given. A simulation example will be given to show the efficiency of the proposed methods.