Robust fault detection for nonlinear discrete-time Markovian jump systems with partly unknown transition probabilities

Abstract

The problem of robust fault detection (RFD) for nonlinear discrete-time Markovian jump systems (MJSs) with partly unknown transition probabilities is investigated in the paper. With the method of T-S fuzzy linearization, the original systems are described as a set of local linear models. 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. A sufficient condition is first established on the stochastic stability using stochastic Lyapunov-krasovskii function, then in the terms of linear matrix inequalities techniques, the sufficient conditions on the existence of RFDO are presented and proved. Finally, A simulation example is given to illustrate that the proposed RFDO can detect the faults correctly and shortly after the occurrence.