Nonfragile $H_{\infty}$ Filtering of Continuous-Time Fuzzy Systems

Abstract

This paper is concerned with the problem of nonfragile <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 for a class of continuous-time fuzzy systems. Attention is focused on the design of a 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 using the quadratic Lyapunov function approach and adding slack matrix variables, sufficient conditions for designing the nonfragile <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 are proposed in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a simulation example will be given to show the efficiency of the proposed design methods.