Distributed adaptive event-triggered fault detection filter of positive semi-Markovian jump systems

This paper presents a distributed fault detection filter (FDF) for positive semi-Markovian jump systems (PSMJSs) based on an adaptive event-triggered mechanism (AETM) scheme. A novel AETM is first proposed for the systems. A weighted fault model is introduced to assist the estimation of the original fault. Utilizing stochastic copositive Lyapunov function (CLF), a distributed FDF whose parameters are designed by virtue of linear programming (LP), is proposed. Under the designed filter, the positivity and stochastic stability with $L_1/L\text{\_}$-gain performance of a fault detection system is reached. The contribution of this paper contains three aspects: (i) An AETM is constructed for the considered systems, (ii) A distributed FDF is designed for the systems, and (iii) The hybrid $L_1/L\text{\_}$-gain performance is achieved with respect to the disturbance and the fault. Two illustrative examples are given for verifying the validity of the results.