Event-Triggered Asynchronous Fault Detection for Stochastically Switched Systems With Sojourn Probabilities

This paper investigates the event-triggered asynchronous fault detection (FD) problem for discrete-time switched systems with sojourn probabilities. We propose a novel asynchronous FD filter (FDF), of which the sojourn probability is related to the mode of the switched system. A hybrid adjusting variables-dependent event-triggered mechanism (ETM) is devised to reduce the waste of network resources. We construct a new Lyapunov function that contains the mode of the switched system and a flexible variable in the ETM. A sufficient condition in terms of matrix inequalities is obtained under which the error dynamics is stochastically stable with a prescribed
$H_{\infty}$
performance. The parameters of the FDF are explicitly given based on the feasible solutions to these matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed event-triggered asynchronous FD method.