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.

中文翻译：

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具有混合链路和时变延迟的双层复用网络下的固定时间外同步通过延迟反馈控制

由系统组成的网络单元可以在固定的建立时间内收敛到相同的行为，称为固定时间同步。本文研究了双层复用网络的定时外同步问题。为了使网络同步，设计了延迟反馈控制器。为了保证固定时间同步，导出了一些充分的准则。控制器和充分的标准可以应用于无向和有向网络。固定建立时间与控制器、网络节点数和节点维度有关。提供了一些数值例子来说明我们结果的有效性。