  Motivated by the development and deployment of large-scale dynamical systems,
often composed of geographically distributed smaller subsystems, we address the
problem of verifying their controllability in a distributed manner. In this
work we study controllability in the structural system theoretic sense,
structural controllability. In other words, instead of focusing on a specific
numerical system realization, we provide guarantees for equivalence classes of
linear time-invariant systems on the basis of their structural sparsity
patterns, i.e., location of zero/nonzero entries in the plant matrices. To this
end, we first propose several necessary and/or sufficient conditions to ensure
structural controllability of the overall system, on the basis of the
structural patterns of the subsystems and their interconnections. The proposed
verification criteria are shown to be efficiently implementable (i.e., with
polynomial time complexity in the number of the state variables and inputs) in
two important subclasses of interconnected dynamical systems: similar (i.e.,
every subsystem has the same structure), and serial (i.e., every subsystem
outputs to at most one other subsystem). Secondly, we provide a distributed
algorithm to verify structural controllability for interconnected dynamical
systems. The proposed distributed algorithm is efficient and implementable at
the subsystem level; the algorithm is iterative, based on communication among
(physically) interconnected subsystems, and requires only local model and
interconnection knowledge at each subsystem.
