Network composition for optimal disturbance rejection

This paper investigates how the topology of a dynamical network affects its robustness against exogenous disturbances. We consider Laplacian-based network dynamics, and we adopt the H2 system norm to measure the robustness of the network against disturbances. For networks arising from the composition of atomic structures, we provide a closed-form expression of the robustness against disturbances, and we identify optimal composition rules. Specifically, we show that networks consisting of multiple atomic structures are less robust than each isolated part, and that robust structures arise by interconnecting nodes of the atomic components with highest degree. Finally, we describe an algorithm for the design of robust composite networks.