Delay-dependent H∞ filtering for singular Markovian jump systems with general uncomplete transition probabilities

Abstract

This paper is devoted to the investigation of the delay-dependent H∞ filtering problem for a kind of singular Markovian jump time-delay systems with general unknown transition probabilities. In this model, the transition rates of the jumping process are assumed to be partly available, that is, some elements have been exactly known, some ones have been merely known with lower and upper bounds, others may have no information to use. Using the Lyapunov functional theory, a stochastically stable filter is designed to guarantee both the mean-square exponential admissibility and a prescribed level of H∞ performance for the singular Markovian jump time-delay systems with general unknown transition probabilities. A sufficient condition is derived for the existence of such a desired filter in terms of linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed theory.