This paper considers the problem of synchronising linear discrete-time agents with a minimum number of communication events. The idea is based on the fact that the synchronous trajectory of all agents is parametrised by the agent model with the initial state as parameter vector. After the agents have reconstructed this parameter vector from their own output and from communicated information, they are able to reach the synchronous trajectory without further interactions. The paper shows that only 2n communication events are necessary, where n denotes the dynamical order of the agent. After this time, all local controllers can be switched to an autonomous mode without communication. The method is illustrated by its application to a vehicle platoon.