Output cluster synchronization of heterogeneous linear multi-agent systems

This paper considers the cluster synchronization problem for coupled agents which are described by heterogeneous linear dynamic models. The aim is to synchronize the outputs of the agent systems belonging to the same cluster. This problem is solved by incorporating a common internal reference system into agent systems belonging to the same cluster while in different clusters the internal reference systems are assumed to have nonidentical linear dynamics. This paper proposes a leaderless control law for each agent, and derives a necessary and sufficient algebraic condition which relates parameters from the interaction graph and the internal models. This condition is shown to be satisfied if the interaction graph admits a directed spanning tree in each cluster and the coupling strengths among agents are strong enough.