A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses.

Summary: In this article, the stability of quaternion‐valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is, Tα<∞ and Tα=∞, which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p‐norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given. [ABSTRACT FROM AUTHOR]