Abstract
A class of large-scale systems with decentralized information structures such as multi-agent systems can be represented by a linear system with a generalized frequency variable. In this paper, we investigate stability of such systems, which is the most fundamental property from the view point of control. Specifically, we first show that the system is stable if and only if all the eigenvalues of the interconnection matrix are in a region on the complex plane specified by the generalized frequency variable. We then provide an algebraic characterization of the stability region in terms of polynomial inequalities. Finally, the complexity properties of the stability region is examined, and they are illustrated by numerical examples.
