Event-Triggered Fault Detection Filter for Positive Semi-Markovian Jump Systems

This paper designs an $L_{1}$ fault detection filter for positive semi-Markovian jump systems with disturbances based on event-triggering scheme. First, an event-triggering strategy is presented in terms of linear inequality and a fault detection filter is proposed. Then, an augmented fault detection system is constructed. Using stochastic copositive Lyapunov function and linear programming, the filter matrices are designed for guaranteeing the positivity and stochastic $L_{1}$ stability of the considered system. One illustrative example is provided to verify the effectiveness of the results in this paper.