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.