The issue of global exponential synchronization is addressed for delayed impulsive and time-varying delayed inertial memristor-based quaternion-valued neural networks (IMQVNNs). First, the concept of the Filippov solution for IMQVNNs is introduced by applying differential inclusion theory. Then, a nonlinear feedback controller is designed in the skew field of quaternions to ensure the realization of global exponential synchronization for IMQVNNs. According to this controller, the global exponential synchronization criteria are established based on the Lyapunov stability theory. Moreover, a corollary for the real-valued system is given to compare with the existing conclusions. Finally, two examples are presented to show the validity of the results.

全局指数同步的问题针对基于延迟的脉冲和时变的基于惯性忆阻器的四元数值神经网络（IMQVNN）。首先，应用微分包含理论介绍了针对IMQVNN的Filippov解决方案的概念。然后，在四元数偏场中设计了一个非线性反馈控制器，以确保实现IMQVNN的全局指数同步。根据该控制器，基于Lyapunov稳定性理论建立了全局指数同步准则。此外，给出了实值系统的推论，以与现有结论进行比较。最后，给出两个例子来说明结果的有效性。