H∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays

The problem of _H∞$H_{\infty }$ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays is investigated in this paper. The transition probabilities under consideration are time-varying, i.e., Markovian chain is nonhomogeneous. By using the Lyapunov functional approach and reciprocally convex technique, a less conservative delay-dependent bounded real lemma is developed in terms of linear matrix inequalities. Moreover, a sufficient condition for the existence of the desired filter which guarantees the stochastic admissibility and the _H∞$H_{\infty }$ performance index of the resulting filtering error system is presented. Numerical examples are employed to show the usefulness of the proposed results.