On network stability, graph separation, interconnection structure and convex shells

We consider a large scale network comprised of heterogeneous dynamical components. We derive conditions on the input/output properties of locally defined subsystems within the network, such that if these are satisfied the entire interconnection is guaranteed to be stable. The conditions are based on appropriately constructed functionals that lead to graph separation. We illustrate how interconnection structure can be exploited when determining the form of these functionals so as to reduce conservatism in the certificates. Interpretations of the stability conditions by means of disjoint convex shells are also discussed.