Controllability of heterogeneous networked MIMO systems

In this study, we investigate the controllability of weighted and directed networks of multi-input-multi-output (MIMO) systems, in which the nodes obey heterogeneous linear time-invariant (LTI) dynamics. In particular, we analyze the effects of the node dynamics, the network topology, the external control inputs and the internal interactions on the controllability of the heterogeneous networked system. We find that the heterogeneous networked system can be controllable even if the network topology is uncontrollable. We derive a necessary and sufficient controllability condition for the heterogeneous networked system. For some special but meaningful cases, we present necessary or sufficient conditions on the node dynamics, the inner interactions, and the network topology to ensure controllability.