Observability and controllability verification in multi-agent systems through decentralized Laplacian spectrum estimation

In this paper we show how the decentralized estimation of the spectrum of a network can be used to infer its controllability and observability properties. The proposed approach is applied to networked multi-agent systems whose local interaction rule is based on Laplacian feedback. We provide a decentralized necessary and sufficient condition for observability and controllability based on the estimated eigenvalues. Furthermore we show an example of application of the proposed method and show that the estimated spectrum can also be envisioned as a tool for decentralized formation identification.