Exponential control design on fixed-time synchronization of fully quaternion-valued memristive delayed neural networks without decomposition

This article mainly explores fixed-time (FXT) synchronization of fully quaternion-valued memristive neural networks (QVMNNs) with generalized delays. Firstly, based on the set-valued mapping theory and the nonsmooth approach, the discontinuity of quaternion-valued memristive connection weights is successfully solved. Next, by introducing the signum function, absolute-like norm and quadratic norm in the quaternion field, a direct non-decomposing method is put forward. Under this framework, several exponential-type controllers are designed, which have only one exponential term and no longer contain the traditional linear part and the powerlaw terms. Compared with designing four real-value controllers, the control schemes proposed in this article are simpler in form. Besides, several criteria of FXT synchronization and the upper bound of the setting time are deduced based on Lyapunov method and Taylor expansion. Lastly, the achieved synchronization results are confirmed via numerical examples.

Automated summary

This article mainly focuses on fixed-time (FXT) synchronization of fully quaternion-valued memristive neural networks (QVMNNs) with generalized delays. The discontinuity issue of quaternion-valued memristive connection weights is effectively solved using set-valued mapping theory and the nonsmooth approach. A direct non-decomposing method is proposed by introducing the signum function, absolute-like norm, and quadratic norm in the quaternion field. Exponential-type controllers with simplified forms are designed, and criteria for FXT synchronization and the upper bound of the setting time are derived. Numerical examples confirm the achieved synchronization results.