New Controllability Conditions for Networked Identical LTI Systems

A new necessary and sufficient condition for the controllability of networked linear time-invariant (LTI) systems is derived, where the network topology is general and the nodes have identical higher-dimensional dynamics. The condition is easier to verify, explicitly illustrating how the network topology, node-system dynamics, external control inputs and inner interactions altogether affect the controllability of the whole networked system. Furthermore, the controllability of specified Cartesian product networks is revisited, revealing that the necessity of the controllability criterion established in [1] does not hold. In view of this, a modified necessary and sufficient condition is established. The effectiveness of the conditions is demonstrated through several examples.