Fault detection of discrete-time delay Markovian jump systems with delay term modes partially available

Abstract

This paper focuses on the fault detection problem for a class of discrete-time delay Markovian jump systems with delay term modes partially available. A crucial but general hypothesis considered here is there is a suitable and effective detector to provide a measurement signal of operation mode of delay term. The fault detection filter used as the residual generator could depend on the original system operation mode or the signal emitted from detector. Via minimizing the error between the residual and fault signal, the problem of fault detection and isolation (FDI) is converted into an H∞ filtering problem and closely related to a probability representing the degree of dependence between the original and measurable signals. An improved Lyapunov function depending on such two operation modes is exploited to study the corresponding problems. Sufficient conditions for the existence of the desired FDI filter are presented in terms of LMIs. When such a probability is uncertain or partially unknown, similar problems are also considered. A practical example is used to demonstrate the effectiveness and superiority of the proposed methods.