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

摘要

This paper is concerned with the problem of finite frequency (FF) H_∞ 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_∞ 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_∞ 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.