Further results on consensus for coupled swarm systems

The motion of the swarm system can be composed of the absolute motion of the swarm as a whole and the relative motion between nodes. Especially for nonlinear swarm systems, their absolute motion remains unknown. This paper considers a synchronization model for continuous-time swarm systems, which can be viewed as a generalized version of the consensus model for multi-agent systems, where node dynamics can be linear or nonlinear, and the coupling function of the state between nodes can also be linear or nonlinear. This paper is dedicated to answer what the specific form of the synchronization function (i.e., the absolute motion of the synchronized swarm system) is, and how to determine the contribution rate of the nodes in the network to the synchronization function. We leverage the state decomposition method to determine the synchronization function. Specifically, the paper illustrates the relationship between the synchronization function and the solution of the isolated node.