Exponential Stabilization Control of Delayed Quaternion-Valued Memristive Neural Networks: Vector Ordering Approach

Abstract

The stabilization control of the quaternion-valued memristive system is investigated in this paper. By starting from the basic quaternion-valued algorithms, the memristive system described by quaternion-valued connection weights is derived. Subsequently, a comprehensive set of results to ensure the existence of the equilibrium point and its stability analysis have been developed. Particularly, vector ordering approach is proposed in this paper, which can be employed to determine the “magnitude” of two different quaternion-valued, and thus the closed convex hull derived by two different quaternion-valued connections can be obtained correspondingly. In the end, the proposed method is substantiated with two numerical examples.