A. Gasparri, G. Oliva, M. Franceschelli and S. Panzieri, "Online Distributed Synchronizability Check for Networks of Interconnected Systems," IEEE MASS 2012, the 9th IEEE International Conference on Mobile Ad hoc and Sensor Systems (The 6th International Workshop on Wireless Sensor, Actuator and Robot Networks - WiSARN2012-Fall) Las Vegas USA, 2012.
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 only depends on the topology, and specifically on the ratio between the algebraic connectivity (second eigenvalue ) and the spectral radius (maximum eigenvalue) of the Laplacian matrix describing 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. Furthermore, decentralized techniques to achieve an agreement on the synchronization parameters are discussed. Simulations results are provided to show the effectiveness of the proposed algorithm.