  The controllability of networks comprising homogeneous multi-input
multi-output linear subsystems with linear couplings among them is examined,
from a modal perspective. The eigenvalues of the network model are classified
into two groups: 1) network-invariant modes, which have very high multiplicity
regardless of the network's topology; and 2) special-repeat modes, which are
repeated for only particular network topologies and have bounded multiplicity.
Characterizations of both types of modes are obtained, in part by drawing on
decentralized-fixed-mode and generalized-eigenvalue concepts. We demonstrate
that network-invariant modes necessarily prevent controllability unless a
sufficient fraction of the subsystems are actuated, both in the network as a
whole and in any weakly-connected partition. In contrast, the multiplicities of
special-repeat modes have no influence on controllability. Our analysis
highlights a distinction between built networks where subsystem interfaces may
be unavoidable barriers to controllability, and multi-agent systems where
protocols can be designed to ensure controllability.
