Delay-distribution-dependent H∞ filtering for linear systems with stochastic time-varying delays

This paper is concerned with the H∞ filtering problem for a class of linear deterministic systems with stochastic time-varying delays, where the desired filter has multiple choices. Firstly, the original delay range is separated into several subintervals, whose inherently stochastic property is described by a Markov process and how to get the corresponding transition rate matrix is also given detailedly. Then, by making full use of each subinterval's delay bound and delay distribution information, new less conservative result on H∞ performance is presented. Based on the obtained criteria, sufficient conditions for the existence of H∞ filter are given as strict linear matrix inequalities. Which filter acting is determined by the current time delay belonging to which subinterval. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.