Decentralized and Compositional Interconnection Topology Synthesis for Linear Networked Systems

We consider networked systems comprised of interconnected sets of linear subsystems and propose a decentralized and compositional approach to stabilize or dissipativate such linear networked systems via optimally modifying some existing interconnections and/or creating entirely new interconnections. We also extend this interconnection topology synthesis approach to ensure the ability to stabilize or dissipativate such networks under distributed (local) feedback control. To the best of the authors’ knowledge, this is the first work that attempts to address the optimal interconnection topology synthesis problem for general linear networked systems. The proposed approach only involves solving a sequence of linear matrix inequality problems (one at each subsystem), and thus, it can be implemented efficiently and scalably in a decentralized and compositional manner. We also include a case study where the proposed interconnection topology synthesis approach is compared with an alternative dissipativity-based approach.