  This paper 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 for 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 neighborhood. The results
show that the availability of local bounds on neighborhoods plays a key role.
