Dynamical system decomposition using dissipation inequalities

James Anderson, André Teixeira, Henrik Sandberg, Antonis Papachristodoulou

Abstract: In this paper we investigate stability and interaction measures for interconnected systems that have been produced by decomposing a large-scale linear system into a set of lower order subsystems connected in feedback. We begin by analyzing the requirements for asymptotic stability through generalized dissipation inequalities and storage functions. Using this insight we then describe various metrics based on a system's energy dissipation to determine how strongly the subsystems interact with each other. From these metrics a decomposition algorithm is described.