Exponentially quasi-synchronization control of quaternion-valued memristive neural networks: matrix measure strategies and Frobenius norm methods

This work explores the exponentially quasi-synchronization control of quaternion-valued memristive neural networks. The entire analysis does not use reduced-order conversion, nor does it involve the separation of real and imaginary parts, but directly focuses on the original system, which preserved the integrity of the quaternion-valued system. First, the definition of x\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{x}$$\end{document}, x is an element of Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x\in \mathbb {Q}$$\end{document} is first introduce, which provides new methods to investigate quaternion-valued systems in a compact form. Second, using Frobenius norm, the derived conclusions contain much more information of the matrix elements compared with the traditional 1-norm or 2-norm. Eventually, numerical examples are carried out to verify the derived schemes.