New Results on $H_{\infty}$ Filtering for Fuzzy Time-Delay Systems

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">infin</sub> fuzzy filtering problem for a class of continuous-time fuzzy systems with time-varying delays. The objective is to design a stable filter guaranteeing the asymptotic stability and 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">infin</sub> performance of the filtering error system. Motivated by the parallel distributed compensation technique, we design a new filter model in this paper. Filter parameter matrices can be obtained from the solution of a convex optimization problem in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired <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">infin</sub> fuzzy filter is given. Two numerical examples are provided to demonstrate the effectiveness and less conservativeness of the proposed design approach.