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

This article addresses the zonotope-based L∞ 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 L∞ performance of the positive state zonotope is analyzed by defining suitable center and radius functions for matched and mismatched intervals, respectively. Then, the permissible MDADT signals and asynchronous controllers are jointly designed to guarantee the stability and L∞ performance for the underlying system. Finally, the effectiveness and advantages of the proposed method are demonstrated through a numerical example.