Topological Controllability of Undirected Networks of Diffusively-Coupled Agents

This paper presents conditions for establishing topological controllability in undirected networks of diffusively-coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our approach differs from well-known structural controllability conditions for linear systems or consensus networks, where controllability conditions are based on edge connectivity (i.e., zero or non-zero edges). Our results first provide a process for merging controllable graphs into a larger controllable graph. Then, based on this process, we provide a graph decomposition process for evaluating the topological controllability of a given network.