A Sufficient Condition for Colored Strong Structural Controllability of Networks

摘要

This paper deals with strong structural controllability of leader/follower networks. In the existing literature on structural controllability of networks, a basic assumption is that the nonzero off-diagonal entries in the matrices in the qualitative class associated with the network graph are completely independent. However, in real world networks, this assumption is not always satisfied. In this paper, we study the situation that some of these entries are constrained to take identical values. This will be formalized using the concept of colored graphs. Furthermore, we consider colored bipartite graphs and establish a necessary and sufficient graph-theoretic condition for the nonsingularity of all matrices in the associated pattern class. We then introduce a new coloring rule and a new concept of zero forcing set. Based on these concepts, we formulate a graph-theoretic condition for strong structural controllability of systems on colored graphs.