Robust fault detection for discrete-time markovian jump linear systems with partly unknown transition probabilities

The problem of robust fault detection (RFD) for discrete-time Markovian jump linear systems (MJLSs) with partly unknown transition probabilities is investigated in the paper. The RFD observer (RFDO) system and the dynamics of error generator are constructed. By introducing some free-weighting matrices, the proposed method leads to less conservatism compared with the existing ones. Moreover, the H
_∞
performance index is proposed to minimize the influence of the unknown disturbances. Sufficient conditions on the existence of RFDO are established and given in terms of LMIs. Finally, a simulation example is given to illustrate that the proposed RFDO can detect the faults correctly and shortly after the occurrence.