On robust H∞ filtering of uncertain Markovian jump time-delay systems

This paper is concerned with the problems of stability analysis, H∞ performance analysis, and robust H∞ filter design for uncertain Markovian jump linear systems with time-varying delays. The purpose is to improve the existing results on these problems. Firstly, a new delay-dependent stability criterion is obtained on the basis of a novel mode-dependent Lyapunov functional. Secondly, a new delay-dependent bounded real lemma (BRL) is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Thirdly, with the new BRL, delay-dependent conditions for the solvability of the addressed H∞ filtering problem are given. All the results obtained in this paper are expressed by means of strict linear matrix inequalities. Three numerical examples are provided to demonstrate the utility of the proposed methods