Controllability of networked MIMO systems

In this paper, we consider the state controllability of networked systems, where the network topology is directed and weighted and the nodes are higher-dimensional linear time-invariant (LTI) dynamical systems. We investigate how the network topology, the node-system dynamics, the external control inputs, and the inner interactions affect the controllability of a networked system, and show that for a general networked multi-input/multi-output (MIMO) system: (1) the controllability of the overall network is an integrated result of the aforementioned relevant factors, which cannot be decoupled into the controllability of individual node-systems and the properties solely determined by the network topology; (2) if the network topology is uncontrollable by external inputs, then the networked system with identical nodes will be uncontrollable, even if it is structurally controllable; (3) with a controllable network topology, controllability and observability of the nodes together are necessary for the controllability of the networked systems under some mild conditions, but nevertheless they are not sufficient.