Fault Detection for Discrete-Time Systems With Fault Signal Happening Randomly: The Markov Approach

Abstract

In this paper, the fault detection problem is considered for a class of discrete-time systems with fault signal happening randomly. First, the random occurrence of fault is described by a Markov approach, which is transformed into some matrices experiencing Markov switchings. By using a fault detection filter as a residual generator, the fault detection and isolation (FDI) problem is transformed into an $H_\infty $ filtering problem. Moreover, a mode-dependent Lyapunov functional is exploited to make its analysis and synthesis and is also named to be a fault-dependent approach. Then, sufficient conditions on the existence of an FDI filter are all provided in terms of linear matrix inequalities, in which two general cases about transition probability matrix are included. Finally, a practical example is used to illustrate the effectiveness and potential application of the developed theoretical results.