Radius Analysis-Based Control for Switched Positive Systems

This article investigates the dynamic output feedback control for switched positive systems with mode-dependent persistent dwell time (MPDT) switching and unmeasurable disturbances. Unlike the previous results, in this article, we propose a radius analysis-based control method. By constructing the time-varying state zonotope and guaranteeing its dual convergence, dynamic output feedback controllers are designed, and then the stability of the closed-loop system and convergent state boundaries are both realized. First, the dual convergence and $\mathcal {L}_{\infty }$ performance are addressed for the positive zonotope by constructing proper mode-dependent radius and center functions. Then, employing the radius analysis-based control method, allowable MPDT signals and a series of controllers are codesigned to ensure the stability of the underlying system. Furthermore, a relaxed method is given to further improve conservatism of the radius analysis based control approach. Finally, an example is taken to certify the effectiveness and merits of our proposed methods.