Finite frequency H∞ filter design for T-S fuzzy systems: New approach

This paper studies the problem of H∞ filter analysis and design for discrete-time Takagi-Sugeno (T-S) fuzzy systems, in a finite frequency (FF) domain. Based on a fuzzy basis dependent Lyapunov function and time domain interpretations of Generalized Kalman Yakubovich Popov (GKYP) lemma, combined with generalised S-procedure, sufficient conditions are developed, guaranteeing that the filtering error system is stable and has a prescribed H∞ attenuation level, over a specified FF domain of the external disturbances. Furthermore, several additional slack variables are introduced to the derived conditions by applying Finsler's lemma twice, which leads to performance improvement and less conservatism in the solution. Thus, new filter design conditions are proposed in the formulation of Linear Matrix Inequality (LMI) terms in three different frequency ranges, (low, middle and high frequencies). A numerical example is given to demonstrate the feasibility, the effectiveness and the less conservatism of the proposed approach in comparison with another solution that appears in the literature.