Connection Between the Passivity Index and Conic Systems

This report covers open-loop conditions that guarantee closed-loop stability of a feedback interconnection of two systems. The traditional solutions for this problem are passivity theory and the small gain theorem. These approaches can be shown to be part of a larger design framework. Two such larger frameworks are the conic systems framework and the passivity index framework. This report shows that these two actually reduce to the same open-loop conditions on the two systems in the interconnection. This connection is shown for the purpose of applying this generalized framework to switched systems. The recent application of passivity to switched systems gives one method of guaranteeing that the feedback interconnection of two switched systems is stable. However, a more general framework is presented in this report that is based on passivity theory but can show stability for the feedback interconnection of systems that aren’t necessarily passive or even stable.