In this paper, we study the quasi-synchronization control for a class of fractional-order quaternion-valued neural networks (QVNNs). Unlike previous studies, the introduce of the reaction–diffusion terms makes the model more comprehensive. It is worth mentioning that in earlier literature, there are rare results based on linear matrix inequality method when using the decomposition method (dividing the system into four real-valued ones) to study the synchronization for QVNNs, which is due to the great challenge posed by the cross-product terms. In this work, we overcome this problem by processing the cross-product term as some free variables and then obtain the quasi-synchronization criterion of the system by linear matrix inequalities (LMI) method, which extends some previous works. Finally, a numerical example is given to support the results of this paper.

在本文中，我们研究了一类分数阶四元值神经网络（QVNNs）的准同步控制。与以往的研究不同，反应-扩散项的引入使模型更加全面。值得一提的是，在早期的文献中，在使用分解法（将系统分成四个实值）研究QVNNs的同步时，很少有基于线性矩阵不等式法的结果，这是由于提出了很大的挑战。由叉积项。在这项工作中，我们通过将叉积项处理为一些自由变量来克服这个问题，然后通过线性矩阵不等式（LMI）方法获得系统的准同步准则，这扩展了之前的一些工作。最后，