Synchronization criteria for quaternion-valued coupled neural networks with impulses.

Abstract

We consider the global exponential synchronization of a category of quaternion-valued coupled neural networks (QVCNNs) with impulses in this article. It makes up for the gap of coupled neural networks with impulses in quaternion. On account of the product of two quaternions cannot be exchanged under normal circumstances, for convenience, we isolate the QVCNN into four real-valued coupled neural networks (RVCNNs) which are converted into an augmented system by defining a new augmented vector. By leveraging a distinctive Lyapunov-Krasovskii function and some matrix inequalities, several sufficient conditions for the global exponential synchronization of the system are attained. Ultimately, two examples are used to prove the validity of the theories in this paper.