Cluster synchronization of inter-cluster nonidentical linear systems under directed nonnegative graphs

This paper aims to achieve cluster synchronization for coupled linear dynamical systems whose models are distinct in different clusters under directed nonnegative graphs. Both static coupling strategies and dynamic coupling strategies are utilized. The static couplings are applicable to interaction graphs where the inter-cluster connections are acyclic, and will render the analysis intractable when inter-cluster connections form cycles. In comparison, the dynamic couplings are shown to be applicable in general graphs. A cluster spanning trees condition is imposed on the interaction graph, and is shown to be necessary and sufficient under acyclic inter-cluster structures. Lower bounds on a weighting factor of the interaction graph are derived under the two coupling strategies, respectively.