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In this study, the reliable H_{∞} filtering problem is studied for discretetime 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 discretetimevarying delay and the infinitedistributed delay. The failures of sensors are quantified by a stochastic variable taking values in a given interval. A discretetime 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 modedependent 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.
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