Robust fault detection of Markovian jump systems with partly unknown transition probabilities

Abstract

A linear full-order robust fault detection observer is designed to solve the robust fault detection problem of Markovian jump systems with partly unknown transition probabilities. Free-connection weighting matrices are introduced to robust fault detection observer design, which reduces the conservatism caused by fixed-connection weighting matrices. A series of linear matrix inequalities (LMIs) which ensure the system's stochastic asymptotic stability are obtained by using the constructed Lyapunov function. Based on that, a sufficient condition for the existence of the robust fault detection observer system is given and proved. Furthermore, an optimization design approach is also derived. A simulation example is given to show that the designed robust fault detection observer can not only detect the faults quickly and sensitively, but also respond robustly to unknown disturbances.