A Generalized Distributed Analysis and Control Synthesis Approach for Networked Systems with Arbitrary Interconnections

We consider the problem of distributed analysis and control synthesis to verify and ensure properties like stability and dissipativity of a large-scale networked system comprised of linear subsystems interconnected in an arbitrary topology. In particular, we design systematic networked system analysis and control synthesis processes that can be executed in a distributed manner at the subsystem level with minimal information sharing among the subsystems. Compared to recent work in the literature, we consider a substantially more generalized problem setup and develop distributed processes to verify and ensure a broader range of properties. We show that optimizing subsystems’ indexing scheme used in such distributed processes can substantially reduce the required information-sharing sessions between subsystems. We also show that sharing information among the neighboring subsystems is sufficient for the proposed distributed processes in some network topologies. Moreover, the proposed distributed processes are compositional and thus allow them to conveniently and efficiently handle situations where new subsystems are being added to an existing network. We also provide significant insights into our approach so that it can be quickly adopted to verify and ensure properties beyond the stability and dissipativity of networked systems. Finally, we provide a numerical example to demonstrate the proposed distributed processes and highlight our contributions.