A distributed Nyquist criterion for heterogeneous networks

We derive a distributed Nyquist type criterion that can certify scalable robust stability for linearly interconnected heterogeneous dynamical systems. The result holds for linear SISO dynamical systems with bidirectional links between them. Unlike previous results of this kind, we allow for otherwise arbitrary interconnection topologies (i.e linear systems on arbitrary underlying undirected graphs). Each agent is required to satisfy a local test that involves only a knowledge of its own dynamic and those of its neighbours; a new agent introduces only an additional such condition hence the stability certificates scale with the network size.