Fault detection filter design for Markov jump systems with persistent dwell-time

This paper addresses the problem of fault detection (FD) for Markov jump systems (MJSs) with time-varying delays. The jumping property presented by system modes is described by the Markov chain and the transition probabilities of the Markov chain are described by adopting the more flexible persistent dwell-time (PDT) switching rule. By introducing a filter to establish a residual system, the problem was converted into an $H_{\mathrm{\infty }}$ filtering problem. The problem is complicated by the coexistence of time constraints in the PDT switching law and time-varying delays. By combining the Lyapunov-Krasovskii (L-K) method and switched system theory, a suitable filter was designed and a new PDT constraint was obtained. Ultimately, a virus mutation system model was used to demonstrate the practicability and effectiveness of the designed FD filter.