Structural Controllability of Undirected Diffusive Networks with Vector-Weighted Edges

In this letter, controllability of undirected networked systems with diffusively coupled subsystems is considered, where each subsystem is of identically fixed general high-order single-input-multi-output dynamics. The underlying graph of the network topology is vector-weighted, rather than scalar-weighted. The aim is to find conditions under which the networked system is structurally controllable, i.e., for almost all vector values for interaction links of the network topology, the corresponding system is controllable. It is proven that, the networked system is structurally controllable, if and only if each subsystem is controllable and observable, and the network topology is globally input-reachable. These conditions are further extended to the cases with multi-input-multi-output subsystem dynamics and matrix-weighted edges, or where both directed and undirected interaction links exist.