New Approach to H∞ Filtering for Fuzzy Systems in Finite Frequency Domain

This paper is concerned with the problem of finite frequency (FF) H-infinity full-order filtering design for discrete-time nonlinear systems, in the Takagi-Sugeno form. We choose basis dependent Lyapunov function and using the finite frequency l(2) gain definition, and the generalized S-procedure lemma, we propose sufficient conditions, ensuring that the filtering error system is stable and has a minimized H-infinity attenuation level in the low-, middle-, and high-frequency domains. In order to linearize and relax the obtained conditions, we apply the Finsler's lemma twice, and we obtain a set of new sufficient conditions for the existence of the H-infinity filter in terms of linear matrix inequalities (LMIs). Then, we show how we can calculate the filter gain matrices by using these conditions. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.