Robust synchronization via set-valued maximal monotone couplings

We explore the use of set-valued coupling laws for the design of robust synchronized behaviors in networks of dynamical systems. Under an incremental dissipativity context, it is shown that coupling systems via maximal monotone mappings leads to synchronization that is robust against matched disturbances. Additionally, it is shown that perfect synchronization of heterogeneous networks with persistent matched disturbances is attained with finite coupling strength but infinite incremental gain on the coupling maps. The real-life implementation of the proposed controllers is studied under the context of practical synchronization via Yosida regularizations. Simulations illustrate the effectiveness of the proposed methods.