Online distributed synchronizability check for networks of interconnected systems

The synchronization problem of a network of interconnected systems has been deeply analyzed by the scientific community. In the case of identical systems, under suitable hypotheses, the synchronization depends on the network topology, and specifically on the ratio between the second smallest eigenvalue (algebraic connectivity) and spectral radius of the Laplacian matrix corresponding to the network topology. In this paper a distributed algorithm for the estimation of such a ratio is given, hence providing a distributed synchronizability check for networks of interconnected systems. Simulations results are provided to show the effectiveness of the proposed algorithm.