Asynchronous fault detection filter of positive Markov jump systems by dynamic event-triggered mechanism

Abstract

This paper explores the design of a positive l1-gain asynchronous non-fragile fault detection filter (FDF) for discrete-time positive Markov jump systems (PMJSs) based on the dynamic event-triggered method (DETM). Due to the effect of positivity on event-triggered mechanisms and non-triviality on stability of discrete-time PMJSs, a new more powerful and generic DETM that can avoid non-triviality is developed. The asynchronous situation between the non-fragile FDF modes and the system modes is effectively managed by employing a hidden Markov model. Then, the solvability criteria for issues of concern are presented by building the copositive Lyapunov function (CLF) with internal dynamic variables (IDV). An alternative sufficient condition is derived based on the obtained results. Subsequently, a co-design project of the expected dynamic event-triggered positive l1-gain asynchronous non-fragile fault detection filter (DETPGAN-FFDF) and the designed DETM is proposed in this paper. Finally, the effectiveness and superiority of the approach are verified by numerical arithmetic examples and practical applications based on pest management.