Exponential stability analysis of quaternion-valued neural networks with proportional delays and linear threshold neurons: Continuous-time and discrete-time cases

摘要

A class of quaternion-valued neural networks (QVNNs) with proportional delays and linear threshold neurons is proposed in this paper. First, by employing Halanay inequality technique and matrix measure method, the global exponential stability of continuous-time QVNNs with proportional delays and linear threshold neurons is studied, and some sufficient conditions are derived to guarantee global exponential stability of the studied continuous-time systems. Then, the discrete-time analogues of the continuous-time QVNNs with proportional delays and linear threshold neurons are formulated and investigated by using the semi-discretization method. The discrete-time analogues are equivalent to the considered continuous-time neural networks, and possess the convergence behaviors of the considered continuous-time systems without any limitation applied to the discretization step size. Finally, some numerical examples are presented to ensure the effectiveness and correctness of the theoretical results obtained. (C) 2019 Published by Elsevier B.V.