H∞ Filter Design for T-S Nonlinear Discrete-Time State-Delayed Systems in Finite Frequency Domain

In this paper, we investigate the problem of filtering for nonlinear (NL) discrete-time (DT) systems with fixed time delay described by Takagi-Sugeno (T-S) fuzzy model. Unlike the results in the literature reported on this subject, our proposed approach consists of designing a stable filter in the finite frequency (FF) domain of noises. For that, new conditions are developed to ensure the IV performance and the stability of the filtering error system in terms of linear matrix inequalities (LMIs). In order to reduce the filtering error and establish less conservative results, we introduce more slack variables by applying the Finsler's lemma twice, and we obtain a set of new sufficient delay-dependent conditions. Numerical example is given to illustrate the effectiveness and the advantage of the proposed approach.