Variable-time impulsive control for bipartite synchronization of coupled complex networks with signed graphs

Abstract

This paper investigates the bipartite synchronization of coupled complex networks (CCNs) with signed graphs via variable-time impulsive (VTI) control. Different from the traditional complex networks, the communication topology between nodes of the complex networks can be either collaborative or antagonistic. In addition, the appearance of impulses is always dependent on each node in the network instead of appearing at fixed instants. Furthermore, by utilizing the B-equivalent technique, the VTI network models can be changed as fixed-time impulsive CCNs. The fixed-time impulsively controlled CCNs can be regarded as the comparison systems of the signed CCNs with variable-time impulses. By 1-norm analytical techniques, several assumptions are derived to guarantee every solution of the coupled error nodes intersect each discontinuous impulsive surface exactly once. Some sufficient conditions with theoretical demonstration are presented to guarantee the bipartite synchronization under mathematical induction. Simulation results are carried out to show the effectiveness of the obtained results.