In this paper, we focus on the synchronization of fractional-order coupled neural networks (FCNNs). First, by taking information on activation functions into account, we construct a convex Lur’e–Postnikov Lyapunov function. Based on the convex Lyapunov function and a general convex quadratic function, we derive a novel Mittag-Leffler synchronization criterion for the FCNNs with symmetrical coupled matrix in the form of linear matrix inequalities (LMIs). Then we present a robust Mittag-Leffler synchronization criterion for the FCNNs with uncertain parameters. These two Mittag-Leffler synchronization criteria can be solved easily by LMI tools in Matlab. Moreover, we present a novel Lyapunov synchronization criterion for the FCNNs with unsymmetrical coupled matrix in the form of LMIs, which can be easily solved by YALMIP tools in Matlab. The feasibilities of the criteria obtained in this paper are shown by four numerical examples.

在本文中，我们专注于分数阶耦合神经网络（FCNN）的同步。首先，通过考虑激活函数的信息，我们构造了凸Lur'e–Postnikov Lyapunov函数。基于凸Lyapunov函数和一般凸二次函数，我们以线性矩阵不等式（LMI）的形式导出了具有对称耦合矩阵的FCNN的新型Mittag-Leffler同步准则。然后，我们为参数不确定的FCNN提出了鲁棒的Mittag-Leffler同步准则。这两个Mittag-Leffler同步标准可以通过Matlab中的LMI工具轻松解决。此外，我们提出了一种新的Lyapunov同步准则，用于LMI形式的具有不对称耦合矩阵的FCNN，可以通过Matlab中的YALMIP工具轻松解决。