Continuously variable duration Markov models for detection delays in linear jump systems

This paper study the effect of detection delays associated with the decisions of fault detection and identification (FDI) processes on the stochastic stability of linear jump systems (LJS). A mathematical representation for the detection delay is developed. Three models have been proposed: the first models detection delay as a homogeneous finite state Markov chain, the second model represents detection delay as a continuous random variable indexed by a finite state Markov chain. The more general case where detection delay is a mixture of different continuous random variables is presented as the third model. Sufficient condition for the stability of LJS with detection delay has been derived. It is shown that the stability of LJS may be lost in the event of large detection delays. A numerical example is used to demonstrate the theoretical results.