Dynamic-Event-Based Fault Detection for Markov Jump Systems Under Hidden-Markov Mode Observation

Abstract

The fault detection (FD) problem is investigated for event-triggered discrete-time Markov jump systems (MJSs) with hidden-Markov mode observation. A dynamic-event-triggered mechanism, which includes some existing ones as special cases, is proposed to reduce unnecessary data transmissions to save network resources. Mode observation of the MJS by the FD filter (FDF) is governed by a hidden Markov process. By constructing a Markov-mode-dependent Lyapunov function, a sufficient condition in terms of linear matrix inequalities (LMIs) is obtained under which the filtering error system of the FD is stochastically stable with a prescribed H_∞ performance index. The parameters of the FDF are explicitly given when these LMIs have feasible solutions. The effectiveness of the FD method is demonstrated by two numerical examples.