L2 - L∞ reduced-order filter design for T-S fuzzy stochastic discrete systems.

This paper investigates the problem of the <inline-graphic></inline-graphic> filtering for discrete-time Takagi-Sugeno fuzzy stochastic systems. The objective is to find new filter design conditions ensuring both the mean square asymptotic stability and prescribed <inline-graphic></inline-graphic> performance of the filtering error system. By means of a fuzzy Lypunov function and by introducing some slack variables through an appropriate use of the projection lemma, new analysis conditions of <inline-graphic></inline-graphic> performance are proposed. Then, the full and reduced-order <inline-graphic></inline-graphic> filter design conditions are proposed in Linear Matrix Inequality form. Finally, to illustrate the proposed approach, simulation and comparison with existing results in the literature are given. [ABSTRACT FROM AUTHOR]