Equivalent Conditions for the Synchronization of Identical Linear Systems over Arbitrary Interconnections

This paper proposes necessary and sufficient conditions for the synchronization of $N$ identical SISO systems, connected through a directed graph. Both the continuous-time case and the discrete-time case are dealt with. These conditions do not require any assumption on the graph and ensure the uniform global exponential stability of the closed attractor that corresponds to the synchronization set, with guaranteed convergence rate.