A fault detection scheme for discrete-time Markov jump linear systems

In this paper, the fault detection (FD) problems for discrete-time Markov jump linear systems (MJLS) are addressed. A scheme for solving FD problem for discrete-time MJLS, which is subject to the Gaussian disturbances, is proposed. The Kalman filter (KF) is used as a residual generator. Once a residual signal is generated, it will be evaluated whether faults occur or not. Residual evaluation function is selected such that the maximum fault detection rate (FDR) is achieved, for a given false alarm rate (FAR). Finally, threshold is computed by using an estimation of the variance of evaluation function in the fault-free case. To demonstrate the performance of this proposed method, a numerical example is given.