Composability and controllability of structural linear time-invariant systems: Distributed verification

Motivated by the development and deployment of large-scale dynamical systems, often comprised of geographically distributed smaller subsystems, we address the problem of verifying their controllability in a distributed manner. Specifically, we study controllability in the structural system theoretic sense, structural controllability, in which rather than 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., the location of zero/nonzero entries in the plant matrices. Towards this goal, we fist provide several necessary and/or sufficient conditions that ensure that the overall system is structurally controllable on the basis of the subsystems’ structural pattern 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 (where every subsystem has the same structure) and serial (where every subsystem outputs to at most one other subsystem). Secondly, we provide an iterative distributed algorithm to verify structural controllability for general interconnected dynamical system, i.e., it is based on communication among (physically) interconnected subsystems, and requires only local model and interconnection knowledge at each subsystem.