摘要：AbstractThis paper provides a connection between stability radius andLσ-gain of positive systems. TheL1-,L2-, andL∞-gains of an asymptotically stable positive system are characterized in terms of stability radii and useful bounds are derived. We show that the structured perturbations of a stable matrix can be regarded as a closed-loop system with unknown static output feedback, which makes it possible to obtain the main results of this paper. In particular, we use the closed-form expressions for stability radii of positive systems to compute theLσ-gains without resorting to solve optimization problems. We also show that positive stabilization with maximum stability radius can be considered as anL2-gain minimization, which can be solved by LMI. This inherently achieves performance criterion and establishes a link to the reported LP formulations. A significant result of this paper is the unique commonality among the optimal state feedback gain matrices in obtainingLσ-gains of the stabilized system. Numerical examples are provided to support the theoretical results.
