New Decentralized $H_{\infty }$ Filter Design for Nonlinear Interconnected Systems Based on Takagi–Sugeno Fuzzy Models

Abstract

In this paper, the problem of H∞ filter design for nonlinear interconnected systems with time-varying delays through Takagi-Sugeno fuzzy models is revisited. Based on the fuzzy line-integral Lyapunov function approach and the reciprocally convex inequality, a delay-dependent decentralized H∞ filter is designed by guaranteeing the asymptotic stability and a prescribed H∞ performance index for the overall filter error system. A new sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities. The present method provides improvements and produces better results than existing ones in the literature. Two examples are given to show the advantages and effectiveness of the proposed results.