Exponential Cluster Synchronization Under Fast Switching Network Topologies: Controllability, Connectivity, and Compactness
Zhiming Li, Ku Du, Xiang Cao, Yijun Zhang · 2024
This research investigates the intricate domain of synchronization problem among multiple agents operating within a dynamic network topology. A pivotal aspect of this paper aims to find the weakest possible conditions to make the coupled system realize cluster synchronization exponentially under fast switching topology framework. By introducing a new variable, the coupled error systems are transformed into controllable error system with perturbations. Then, we can find that the coupled system could achieve cluster synchronization if the system is controllable; the communication topology switches fast enough and the coupling strength is sufficiently robust. To investigate the necessary of above three conditions, several sufficient conditions are proved to ensure the coupled system achieve cluster synchronization under fast switching topology. Furthermore, this paper culminates in the incorporation of contraction theory and an invariant manifold, demonstrating that the switching topology has an average and state matrices are controllable, which are also imperative for achieving cluster synchronization. Finally, we introduce three simulations to validate the efficacy of the proposed approach and theory.