Sampled-Data-Based Hybrid Dynamic Event-Triggered Control of Positive Markov Jump Systems

The letter studies the sampled-data-based (S-D-B) hybrid dynamic event-triggered control issue of positive Markov jump systems (PMJSs). First, taking into account positivity, a new S-D-B hybrid dynamic event-triggered method (ETM) in the shape of 1-norm is proposed, which can not only further alleviate communication burden but also avoid Zeno behavior. Furthermore, the ETM presented in this letter incorporates two internal dynamic variables, thereby enabling more flexible adjustment of resources. Utilizing the new ETM, an interval approach is introduced to analyze the positivity of closed-loop systems. By employing a co-positive Lyapunov functional (CLF) with looped-functional, a sufficient criterion is derived to ensure the stability of closed-loop systems, and an expected controller design scheme is provided in this letter. Finally, the feasibility and superiority of the proposed 1-norm-form S-D-B hybrid dynamic ETM are illustrated by an example.