New approach to delay‐dependent <i>H</i> _∞ filtering for discrete‐time Markovian jump systems with time‐varying delay and incomplete transition descriptions

Abstract

This study is concerned with the delay‐dependent H ∞ filter design for a class of discrete‐time Markovian jump linear systems (MJLSs) with time‐varying delay and incomplete transition descriptions. The considered systems with incomplete transition descriptions cover the MJLSs with known transition probabilities (TPs), partially unknown TPs and uncertain TPs, which are more general. A new equivalent model is proposed for the original MJLSs by employing a two‐term approximation method, which formulates the filtering problem in the framework of input–output stability. Based on a Markovian Lyapunov–Krasovskii functional combined with the scaled small gain theorem, a new delay‐dependent bounded real lemma for the underlying systems is established. It is shown that by using a linearisation technique, the corresponding full‐ and reduced‐order H ∞ filter design is cast into a convex optimisation problem in terms of linear matrix inequalities. Finally, simulation examples are provided to illustrate the effectiveness and less conservatism of the proposed approach.