A Zonotope-Based Event-Triggered Control Approach for Asynchronously Switched Positive Systems

This article addresses the zonotope-based ${\mathcal {L}}_{\infty }$ event-triggered control for switched positive systems with frequent asynchronism and interval uncertainties. In view of the advantages of zonotope in set description, we extend it to the set-based control, propose a novel zonotope-based control method, and further consider the typical model uncertainty and frequent asynchronism. First, by introducing a 1-norm-based event-triggered scheme, the time-varying state zonotope is established based on the closed-loop system and event-triggering conditions. Second, the dual convergence and ${\mathcal {L}}_{\infty }$ performance of the positive state zonotope is analyzed by defining suitable center and radius functions for matched and mismatched intervals, respectively. Then, the permissible mode-dependent average dwell time signals and asynchronous controllers are jointly designed to guarantee the stability and ${\mathcal {L}}_{\infty }$ performance for the underlying system. Finally, the effectiveness and advantages of the proposed method are demonstrated through a numerical example.