Fixed-time outer synchronization under double-layered multiplex networks with hybrid links and time-varying delays via delayed feedback control

The units of networks, composed of systems, may converge to the same behavior in a fixed settling time, known as fixed-time synchronization. In this paper, the problem of fixed-time outer synchronization of double-layered multiplex networks is studied. To synchronize the networks, delayed feedback controllers are designed. To guarantee the fixed-time synchronization, some sufficient criteria are derived. The controllers and sufficient criteria can be applied to undirected and directed networks. The fixed settling time is related to controllers, the number of nodes for networks, and the dimension of node. Some numerical examples are provided to illustrate the effectiveness of our results.