  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, quite different from the
familiar notion of consensus or formation controllability; 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. For a networked system with single-input/single-output (SISO) LTI
nodes, we present precise necessary and sufficient conditions for the
controllability of a general network topology.
