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 \(\sqrt{x}\) $\sqrt{x}$ , \(x\in \mathbb {Q}\) $x\in \mathbb{Q}$ 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.