Fault detection for discrete-time Markov jump linear systems with partially known transition probabilities

In this paper, the fault detection problem for a class of discrete-time Markov jump linear system (MJLS) with partially known transition probabilities is investigated. The proposed class of systems is more general, which relaxes the traditional assumption in Markov jump systems that all the transition probabilities must be completely known. A residual generator is constructed and the corresponding fault detection and isolation (FDI) problem is formulated as an H
_¿
filtering problem by which the error between residual and fault are minimized in the H
_¿
sense. The LMI-based sufficient conditions for the existence of FDI filter are derived. A numerical example is given to illustrate the effectiveness and potential of the developed theoretical results.