In this paper, the finite-time synchronization (FTS) problem of fractional-order multiplex networks with internal delay, intra- and inter-layer coupling delays, and uncertain intra- and inter-layer coupling matrices is studied. A new hybrid controller, composed of an impulsive controller and a quantized controller, is designed to achieve FTS for the considered network in order to save control resources and reduce the burden of the network. Based on the fractional-order Lyapunov function method, utilizing the fractional-order impulsive finite-time inequality and other inequality methods, several fresh sufficient conditions for the synchronization of the fractional-order uncertain multiplex network (FOUMN) with multiple time-varying delays in an explicitly estimated finite time are obtained. These sufficient criteria also reflect that the FTS of the network is related to its topology, quantization parameters, the order of the fractional derivative, and the impulse function. Lastly, two numerical examples confirm that the theoretical findings are valid.

中文翻译：

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具有多个时变延迟的分数阶不确定多路复用网络有限时间同步的量化混合脉冲控制


本文研究了具有内部延迟、层内和层间耦合延迟以及不确定的层内和层间耦合矩阵的分数阶多路复用网络的有限时间同步 （FTS） 问题。一种新的混合控制器，由脉冲控制器和量化控制器组成，旨在实现所考虑的网络的 FTS，以节省控制资源并减轻网络负担。基于分数阶 Lyapunov 函数方法，利用分数阶脉冲有限时间不等式和其他不等式方法，获得了分数阶不确定复用网络 （FOUMN） 在显式估计的有限时间内具有多个时变延迟同步的几个新的充分条件。这些充分的标准还反映了网络的 FTS 与其拓扑、量化参数、分数导数的顺序和脉冲函数有关。最后，两个数值示例证实了理论发现是有效的。