Controllability Matrix Analysis of Structured Networks: A Tight Lower Bound on the Dimension of Controllable Subspace

Network controllability in structured networks, characterized by edge weights as either zero or non-zero, is an emerging research area. This field has grappled with determining the dimension of the controllable subspace. From a graph-theoretical perspective, our study offers an intuitive analysis of the controllability matrix for structured networks. We categorize our analysis based on networks with single and multiple leaders and propose graph-theoretical conditions to determine the tight lower bounds of the controllable subspace. Our results provide a solid foundation for analyzing and designing complex networked systems.