Robust L2−L∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

Abstract This paper is devoted to the problem of robust L2–L∞ filtering for a class of stochastic systems with both discrete and distributed time‐varying delays. The objective is to design a full‐order filter such that the resulting filtering error system is stochastically asymptotically stable with a prescribed L2–L∞ performance satisfied. Delay‐dependent sufficient condition for the existence of the filter is obtained in terms of linear matrix inequalities (LMIs). And the filter design method is proposed, while the explicit expression for the desired filter is also given. Numerical examples are included to illustrate the benefit and the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society