Intracluster Synchronization of Linear Networks Over Finite Fields

This article investigates the intracluster synchronization problem for linear networks over finite fields. By using the technique of linear transformations and novel invariant subspaces of linear systems over finite fields, several necessary and sufficient conditions for the intracluster synchronization of linear networks over finite fields are proposed. In particular, the obtained results are applicable to verify the complete synchronization of linear networks over finite fields. Finally, some numerical examples are given to illustrate our theoretical results.