Graph-Theoretic Analyses of MIMO Channels in Diffusive Networks

Abstract

In this work, we characterize the finite-zero and infinite-zero structure of a multi-input multi-output channel in a standard model for network synchronization. To do so, we first develop an algebraic analysis of the zeros based on a input-to-output transformation known as the special coordinate basis. This decomposition then allows us to develop topological results on the zeros, i.e. characterizations in terms of the network graph and the input/output locations relative to the graph. Specifically, our results show how the relative locations and interactions among multiple input-output pairs in a network influence the locations of the finite and invariant zeros. As a whole, the study contributes to the analysis of dynamical networks from an input-output perspective, rather than only in terms of internal or emergent behaviors.