Extended passive filtering for discrete-time singular Markov jump systems with time-varying delays

•An extended passive filtering problem for a class of discrete-time singular Markov jump systems with time-varying delays.•Design of a general filter which contains the mode-independent part and the mode dependent part to address the filtering problem.•Three illustrative example shows that the presented methods are effective and applicable.

In this paper, the extended passive filtering problem is investigated for a class of discrete-time singular Markov jump systems (SMJSs) with time-varying delays. Our attention is focused on the design of a general filter which contains the mode-independent part and the mode-dependent part to address the filtering issue. By employing some novel inequalities based on Abel lemma, some sufficient conditions which ensure the considered SMJSs to be stochastically admissible with a mixed H∞H∞ and passive performance γ are established. Based on the conditions, an explicit expression for the desired filter is given. Two numerical examples and a dynamical Leontief model of economic systems are given to demonstrate the reduced conservatism and effectiveness of the presented general filter technique.