On controllability of linear systems from a graph-theoretic perspective
Qi Xiao · Chinese Control Conference · 2012
In this paper, we consider the controllability problem of linear systems from a graph-theoretic perspective. Our aim is to characterize the interconnection graph of a controllable linear system and discuss the relationship between controllability and connectivity. We have derived sufficient and necessary conditions for controllability and connectivity using eigenvalues and eigenvectors of the graph. In particular, we prove that for a regular interconnection graph, controllability implies connectivity.