Fault Detection for State-delay Fuzzy Systems Subject to Random Communication Delay

This paper is concerned with the problem of fault detection for discrete-time state-delay fuzzy systems. It is assumed that the output measurements are subject to random communication delay. The random communication delay is modeled as a finite state Markov process, and it is assumed that the transition probabilities are partially known. The problem addressed is the design of a delay-mode-dependent fuzzy fault detection filter, which is used as a residual generator, such that the estimation error between residual and fault (or, more generally, weighted fault) is as small as possible. Based on a fuzzy Lyapunov functional and Finsler’s Lemma, a delay-dependent sufficient condition for the solvability of the problem is established. The fault detection filter parameters can be obtained by solving a set of linear matrix inequalities. A numerical example is given to illustrate the efficiency of the proposed approach.