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

This paper investigates the problem of the $ L_{2}-L_{\infty } $ L2−L∞ 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 $ L_{2}-L_{\infty } $ L2−L∞ 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 $ L_{2}-L_{\infty } $ L2−L∞ performance are proposed. Then, the full and reduced-order $ L_{2}-L_{\infty } $ L2−L∞ 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.