Cluster Synchronization of Finite-Field Networks
研究了有限域网络的簇同步问题，利用代数状态空间表示和矩阵半张量积，将簇同步转化为状态轨迹的集合稳定性，并给出了充要条件，适用于领导者-跟随者同步和群一致性检查。
This technical paper investigates the cluster synchronization of finite-field networks (FFNs) based on the algebraic state space representation. By resorting to the semi-tensor product of matrices, the cluster synchronization of an FFN can be completely converted into the set stability of state trajectory. Then, a necessary and sufficient condition for the cluster synchronization of FFNs is obtained based on the invariant subset and one-step transition matrix. In particular, the obtained results are applicable to check the leader-follower synchronization and group consensus of FFNs. Finally, a numerical example is given to illustrate the feasibility of the obtained results.