Quasi-projective synchronization of discrete-time fractional-order quaternion-valued neural networks

Abstract

In this article, without decomposing the quaternion-valued neural networks (QVNNs) into two complex-valued subsystems or four real-valued subsystems, quasi-projective synchronization of discrete-time fractional-order QVNNs is investigated. To this end, the sign function for quaternion number is introduced and some related properties are given. Then, two inequalities are built according to the nabla fractional difference and quaternion theory. Subsequently, a simple linear quaternion-valued controller is designed, and some synchronization conditions are given by means of our created inequalities. Finally, numerical simulations are given to prove the feasibility and correctness of the theoretical results.