Reliable H ∞ filtering for discrete-time singular systems with randomly occurring delays and sensor failures

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Abstract
In this study, the reliable H∞ filtering problem is studied for discrete-time singular systems with randomly occurring delays and sensor failures. Two stochastic variables, that are mutually independent but obey the Bernoulli distribution, are introduced to govern the random occurrences of the discrete-time-varying delay and the infinite-distributed delay. The failures of sensors are quantified by a stochastic variable taking values in a given interval. A discrete-time homogeneous Markov chain is used to represent the stochastic behaviour of sensor failures. The main purpose of the addressed reliable H∞ filtering problem is to design a reliable mode-dependent filter such that the filtering error dynamics is not only stochastically admissible but also achieves a prescribed H∞ performance level. A sufficient condition is first established for the existence of the desired filter, and then, the corresponding solvability condition for the desired filter gains is established. The case of Markov chain with partially unknown transition probabilities is also considered. A numerical example is provided to illustrate the effectiveness of the proposed method.