Quantitative analysis of passive systems interconnected on graphs

Abstract

This paper addresses quantitative performance analysis of an interconnected passive system. The passivity property, which provides a unified and abstracted description of dynamical systems, plays an important role for qualitative stability analysis of interconnected large-scale systems. In this paper, quantitative performance is further evaluated for the interconnected passive system. To this end, a performance-characterizing parameter is integrated into the conventional passivity. Then, by using the parameter, the L₂-gain of the entire interconnected system is evaluated. Further assuming that the interconnection rule is described by a graph, more detailed performance analysis and its reinforcement via network expansion are studied.