Matrix measure-based exponential stability and synchronization of Markovian jumping QVNNs with time-varying delays and delayed impulses

Abstract

<p>This article explored the topics of global exponential stability and synchronization issues of a type of Markovian jumping quaternion-valued neural networks (QVNNs) that incorporate delayed impulses and time-varying delays. By utilizing the matrix measure strategy and delayed differential inequality techniques with an impulsive factor, several effective and practical criteria can be established to confirm that the impulsive QVNNs in question can achieve exponential synchronization with the given response system. Furthermore, the contained exponential convergence rate can be clearly presented. Notably, derived criteria are straightforward to verify and implement in real-world applications. In the end, to demonstrate the accuracy and effectiveness of achieved theoretical findings, one numerical example with an explanation was presented.</p>