Diffusive coupling as a quadratic constraint: Synchronization and stability in heterogeneous networks

This paper studies synchronization of heterogeneous multi-agent networks from the perspective of absolute stability theory. We consider networks of nonlinear agents coupled via simple diffusive protocols and ask: how much can the classical passivity assumption on the agents be relaxed while retaining a verifiable, fully distributed synchronization criterion? We show that passivity can be replaced by the strictly weaker property of input feedforward passivity (IFP) – the ability to be rendered passive by a special parallel feedforward compensator. The key idea is a quadratic constraint satisfied by the diffusive coupling protocol. This relaxation becomes especially pronounced in discrete time, where even the first-order integrator fails to be passive yet is IFP. We develop synchronization criteria for networks of heterogeneous IFP agents in both continuous and discrete time within a unified dissipativity framework, and further show that the presence of sufficient damping in a subset of agents ensures global output stability of the coupled network. The results are applied to cooperative adaptive cruise control for vehicle platoons