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

This paper explores the design of a positive l 1 -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 l 1 -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. • In terms of positivity, an LP form of DETM for discrete-time PMJS is developed, which may further reduce data transmission and eliminate non-triviality. Besides, the DETM proposed in the paper covers the static event-triggered method (SETM), which is more versatile. • Considering the asynchrony between PMJSs and FDF, the HMM is introduced to address this dilemma effectively. • By constructing the copositive Lyapunov function with internal dynamic variables, a stability criterion is derived to guarantee that the augmented system is positive and stochastically stable with l1-gain performance. Based on the obtained criterion, we give another sufficient condition. • The required co-design scheme between DETPGAN-FFDF and DETM proposed in this paper is implemented, where the design of the non-fragile FDF eliminates the potential impact of faults or fluctuations on the FDF's performances. In addition, the merits of the proposed DETM and its influence on fault detection are analyzed in detail with numerical examples. [ABSTRACT FROM AUTHOR]