Robust H∞ Filtering for Fuzzy Time-Delay Systems

Abstract

This paper is concerned with robust H∞ filtering for uncertain fuzzy time-delay systems. Robust filtering conditions and a design method of robust H∞ filter are given. A system that is considered in this paper is an uncertain fuzzy system with time-delays in state and output. The time-delay is assumed to be either known constant or unknown time varying. The parameter uncertainties that come into the system are time varying and describe identification error between a real system and its mathematical model. Our approach employs a Lyapunov functional combined with the parameterized model transformation method and the generalized free weighting matrix method. This generalization leads to a generalized robust H∞ filtering condition that is given in terms of linear matrix inequalities. Moreover, based on such a condition, robust H∞ filtering methods for uncertain fuzzy systems with time-delays are given. A numerical example is given to illustrate our robust H∞ filtering methods.