In this paper, the global robust synchronization and synchronization in finite time are considered for fractional-order hybrid coupling complex dynamical networks (CDNs), where the growth of dynamic nodes is discontinuous, and subjected to a quadratic polynomial. Firstly, a convergence principle in finite time is developed for fractional-order nonlinear systems with discontinuous right-hand side. Secondly, a suitable discontinuous controller without the terms of time delays is designed, and the global robust synchronization condition is addressed in the terms of linear matrix inequalities (LMIs) by applying Lyapunov functional approach, inequality analysis technique, and Clarke’s non-smooth analysis method. In addition, the global robust synchronization goal in finite time is achieved by utilizing the developed convergence principle. Moreover, the upper bound of the settling time for the global robust synchronization in finite time is explicitly evaluated. Finally, the feasibility of the proposed design scheme and the validity of theoretical results are verified by two numerical simulation examples.

在本文中，考虑了分数阶混合耦合复杂动力学网络（CDN）的全局鲁棒同步和有限时间同步，其中动态节点的增长是不连续的，并且服从二次多项式。首先，针对右侧不连续的分数阶非线性系统，提出了有限时间的收敛原理。其次，设计了一种合适的不具有时间延迟的不连续控制器，并通过应用Lyapunov函数方法，不等式分析技术和Clarke的非光滑分析方法，以线性矩阵不等式（LMI）解决了全局鲁棒同步条件。 。此外，利用开发的收敛原理可以在有限时间内实现全局鲁棒同步目标。此外，明确评估了有限时间内全局鲁棒同步的建立时间的上限。最后，通过两个数值算例验证了所提设计方案的可行性和理论结果的有效性。