Controllability of Directed Networked MIMO Systems With Heterogeneous Dynamics

This article studies the controllability of networked multi-input-multi-output (MIMO) systems, in which the network topology is weighted and directed, and the nodes are heterogeneous higher-dimensional linear time-invariant (LTI) dynamical systems. The primary objective is to search for controllability criteria beyond those already known for networks with homogeneous dynamics. The focus is on the effects of the network topology, node dynamics, external control inputs, as well as the inner interactions on the network controllability. It is found that a network of heterogeneous systems can be controllable even if the underlying network topology is uncontrollable. The finding, thus, unravels another fundamental property that affects the network controllability—the heterogeneity of the node dynamics. A necessary and sufficient condition is derived for the controllability of networked MIMO LTI systems with heterogeneous dynamics. For some typical cases, necessary and/or sufficient controllability conditions are specified and presented on the node dynamics, inner interactions, as well as the network topology. Some examples are given for illustration and verification.