Fuzzy H<inf>∞</inf> filtering for nonlinear singularly perturbed systems with time-varying delay

Abstract

This paper investigates the problem of designing fuzzy H ∞ filter for a class of nonlinear singularly perturbed systems (SPSs) with time-varying delay in states. The considered system is approximated by a Takagi-Sugeno (T-S) fuzzy model. By using linear matrix inequality (LMI) methods, we give a e-independent sufficient condition for the existence of fuzzy H ∞ filter such that, the resulting filtering error system is globally stable with guaranteed H ∞ performance for sufficiently small e. The gains of filter are obtained by solving a set of e-independent LMIs, and therefore the ill-conditioned problem caused by e can be easily avoid. The proposed method can be applied to both standard and nonstandard nonlinear SPSs. A numerical example is provided to illustrate the effectiveness of the developed method.