Sufficient Conditions on Observability Grammian for Synchronization in Arrays of Coupled Linear Time-Varying Systems

Synchronizability of stable, output-coupled, identical, linear time-varying systems is studied. It is shown that if the observability grammian satisfies a persistence of excitation condition, then there exists a bounded, linear time-varying feedback law that yields exponential synchronization for all fixed, asymmetrical interconnections with connected graphs. Also, a weaker condition on the grammian is given for asymptotic synchronization. No assumption is made on the strength of coupling between the systems.