Improved finite frequency H∞ filtering for Takagi-Sugeno fuzzy systems

Abstract

This paper investigates the design problem of H∞ filtering for discrete nonlinear systems in the Takagi-Sugeno (T-S) form. Our aim is to design a new filter guaranteeing an H∞ performance level in specific finite frequency (FF) ranges. Using the well-known generalised Kalman Yakubovich Popov lemma, Finsler's lemma, sufficient conditions for the existence of H∞ filters for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). Two examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.