Finite-time synchronisation of completely coupled agents

The paper considers the problem of synchronising linear discrete-time agents within a finite time interval. The agents can measure only the outputs to be synchronised. The main result is a controller structure for which the agents synchronise within at most 2n time steps, where n is the dynamical order of the agents. The local controllers are composed of a dead-beat observer for the local states and a dead-beat state feedback. The result shows that for the standard synchronisation problem without disturbances, which is the subject of the majority of papers about synchronisation and consensus, a feedback controller can be found that does not only reach asymptotic synchronisation but moves all agents in finite time onto the synchronous trajectory. The result is illustrated by its application to distance control of a vehicle platoon.