A deterministic gossiping algorithm for the synchronization of multi-agent systems∗

The main objective of the synchronization of multi-agent systems is the asymptotic convergence of the agents towards a common trajectory. This paper considers the synchronization of linear discrete-time agents over a network in which only point-to-point connections are allowed. The main result is a new control algorithm designed to ensure asymptotic synchronization of the networked agents. The control algorithm of each agent works in the following steps: (i) establish a coupling to a neighboring agent that is currently not connected to another agent. (ii) synchronize the coupled agents in finite time and search for another agent to be coupled. A deterministic coupling of the agents is required and achieved by the use of a periodically changing coupling sequence. Considering the synchronization of integrators reveals the similarity to a gossiping algorithm. However, this paper extends the results reported in the literature because a necessary and sufficient condition for the synchronization of discrete-time multi-agent systems with arbitrary linear dynamics is presented.