Controllability of Multiweighted Directed Dynamical Networks

This article studies the controllability of multiweighted directed dynamical networks, where the nodes are heterogeneous linear time-invariant dynamical systems and the connections are characterized by multiple weight attributes. For such multiweighted networks to be controllable, some necessary and sufficient conditions are established. To identify different weight attributes, a multiweighted network is decomposed into multiple single-weighted networks, and then their relationships are characterized with respect to their controllability. Furthermore, the controllability of multiweighted networks with some typical topologies is studied in detail, for which specific controllability conditions are derived. Simulations are presented to verify the theoretical results. This research reveals the impact of multiple weight attributes, node dynamics, and inner coupling structures on the controllability of the integrated multiweighted networks, demonstrating that the controllability of multiweighted networks is remarkably distinct from single-weighted networks.