Quasi-Synchronization for Fractional-Order Reaction-Diffusion Quaternion-Valued Neural Networks: An LMI Approach

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.