In this article, we investigate the cluster synchronization in finite time for nonlinear complex dynamical networks (CDNs) with hybrid couplings via aperiodically intermittent control. First, a new lemma with respect to the convergence in finite time is developed for the nonnegative continuous functions. Second, the classification controller, which is dependent of the coupling of the dynamic nodes among different clusters, is designed to realize the cluster synchronization goal. Third, by means of the Lyapunov functional approach, the inequality analysis technique, and the proposed lemmas, the global cluster synchronization conditions in finite time are addressed in terms of linear matrix inequalities (LMIs) for CDNs via discontinuous feedback control scheme with integral terms. Moreover, the global cluster synchronization conditions in finite time is also achieved in the form of LMIs for CDNs with hybrid couplings via aperiodically intermittent control. In addition, the settling time, which is closely related to the topological structure of networks and the maximum ratio of the rest width to the aperiodic time span, is estimated accurately. Finally, the effectiveness of theoretical results is verified by two simulation examples.

中文翻译：

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具有非周期性间歇控制的混合耦合复杂动力网络在有限时间内的全​​局集群同步

在本文中，我们通过非周期性间歇控制研究了具有混合耦合的非线性复杂动态网络（CDN）在有限时间内的集群同步。首先，针对非负连续函数，提出了关于有限时间收敛的新引理。其次，设计了依赖于不同集群之间动态节点耦合的分类控制器，以实现集群同步目标。第三，借助Lyapunov函数方法，不等式分析技术和拟议的引理，通过具有积分项的不连续反馈控制方案，通过CDN的线性矩阵不等式（LMI）解决了有限时间内的全​​局群集同步条件。此外，有限时间内的全​​局集群同步条件也可以通过非周期性间歇控制以带有混合耦合的CDN的LMI形式实现。此外，准确估计与网络的拓扑结构以及静止宽度与非周期性时间跨度的最大比率密切相关的建立时间。最后，通过两个仿真实例验证了理论结果的有效性。