Fault detection for singular networked control systems with randomly occurring delays and partially known distribution transmission delays

Abstract

In this paper, the fault detection problem is discussed for a class of discrete-time singular networked control systems with randomly occurring delays and network-induced delays. The considered randomly occurring delays include the multiple state delays and the infinite-distributed delay. Both of them are assumed to occur in random ways, which are governed by two independent stochastic variables satisfying the Bernoulli binary distribution. Network-induced delays are modeled as a discrete-time homogeneous Markov chain, and the transition probabilities of the Markov chain are partially known. A stochastic Lyapunov functional is constructed to design a full-order fault detection filter guaranteeing that the fault detection dynamics is stochastically admissible with a prescribed $H_{\infty }$ performance index. Hence, the fault detection filter design problem is converted into a convex optimization problem in terms of a set of linear matrix inequalities. If these linear matrix inequalities are feasible, the corresponding parameters of the designed fault detection filter are determined. Finally, a numerical example is addressed to demonstrate the effectiveness of the developed method.