L2–L∞ filtering for a class T-S fuzzy discrete systems under stochastic perturbation

Abstract

This work tackles the L 2 –L ∞ filter design problem for the discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems. The approach based on the (T-S) fuzzy systems, and the objective is to provide a new design with sufficient condition via LMI procedure. Less conservative results are obtained through the use of the projection lemma to introduce additional free matrices. These tools allow to obtain a full-order filter design with extra degree of freedom in order to optimize the L 2 –L ∞ performance. At the end, several examples are used to illustrate the efficiency of the proposed approach.