Synchronisation of Linear Agents over a Time-Varying Random Network

This paper addresses the problem of synchronising linear autonomous agents whose local control units are connected over a time-varying random communication network. The network switches among a set of random graphs, each of which is active within a fixed time interval. The main result shows that if the switching time is sufficiently small, the autonomous agents synchronise almost surely provided that the averaged communication network ensures the synchronisation of the agents. The length of the minimum time interval is given depending on the parameters of the local control units and of the random graphs. Furthermore, the synchronisation time of the agents is estimated.