Delay-dependent H∞ filtering for discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities

This paper is concerned with the H∞H∞ filtering design for a class of discrete-time singular Markovian jump systems with time-varying delay and partially unknown transition probabilities. The class of systems under consideration is more general and covers the singular Markovian delay systems with completely known and completely unknown transition probabilities as two special cases. A mode-dependent filter is constructed and by defining an appropriate stochastic Lyapunov functional combined with using the discrete Jensen inequality, a delay-dependent bounded real lemma (BRL) for the considered systems is established in terms of linear matrix inequalities (LMIs). Based on this, a sufficient condition on the existence of the desired filter which guarantees the admissibility and the H∞H∞ performance of the corresponding filtering error system is presented by employing the LMIs technique. Some numerical examples are provided to illustrate the effectiveness of the developed theoretical results.