The role of local bounds on neighborhoods in the network for scale-free state synchronization of multi-agent systems

This article provides necessary and sufficient conditions for the existence of solutions to the state synchronization problem of homogeneous multi-agent systems (MAS) via scale-free linear dynamic non-collaborative protocol in both continuous and discrete time. These conditions guarantee for which class of MAS, one can achieve scale-free state synchronization. We investigate protocol design with and without utilizing local bounds on the neighborhood of agents. The results shows that the availability of local bounds on neighborhoods plays a key role.