Decentralized and Compositional Interconnection Topology Synthesis for Linear Networked Systems

Abstract: In this paper, 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 linear networked systems 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 linear networked systems. The proposed approach in this paper only involves solving a sequence of linear matrix inequality problems (one at each subsystem). Thus, using standard convex optimization toolboxes, it can be implemented efficiently and scalably in a decentralized and compositional manner. Apart from many generic linear networked systems applications (e.g., power grid control), a unique application for the proposed interconnection topology synthesis approach is in generating random stable (or dissipative, stabilizable, dissipativate-able) linear networked systems for simulation purposes. We also include an interesting case study where the proposed interconnection topology synthesis approach is compared with an alternative approach that only uses dissipativity information of the involved subsystems.