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Upper and Lower Bounds for Controllable Subspaces of Networks of Diffusively Coupled Agents

This technical note studies the controllability of diffusively coupled networks where some agents, called leaders, are under the influence of external control inputs. First, we consider networks where agents have general linear dynamics. Then, we turn our attention to infer network controllability from its underlying graph topology. To do this, we consider networks with agents having single-integrator dynamics. For such networks, we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions, respectively. We also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders.