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Stability analysis of commutative quaternion valued neural network with time varying delays
- Chinese Journal of Intelligent Science and Technology Vol. 2, Issue 1, Pages: 80-87(2020)
- 作者机构：
1. 重庆交通大学数学与统计学院，重庆 400074
2. 西藏大学理学院，西藏 拉萨 850000
3. 南京航空航天大学计算机科学与技术学院，江苏 南京 210016
- 作者简介：
- 基金信息：
DOI：10.11959/j.issn.2096-6652.202009
CLC： O175.13-
Published Online：2020-03，
Published：20 March 2020
- 稿件说明：
移动端阅览
Dongyuan LIN, Xiaofeng CHEN, Wentao SUN, et al. Stability analysis of commutative quaternion valued neural network with time varying delays[J]. Chinese journal of intelligent science and technology, 2020, 2(1): 80-87.
Dongyuan LIN, Xiaofeng CHEN, Wentao SUN, et al. Stability analysis of commutative quaternion valued neural network with time varying delays[J]. Chinese journal of intelligent science and technology, 2020, 2(1): 80-87. DOI： 10.11959/j.issn.2096-6652.202009.
摘要
针对传统的四元数乘法运算不满足交换律的问题，介绍了一种可交换四元数，同时建立一种交换四元数神经网络（CQVNN），并对CQVNN的渐近稳定性进行研究。研究过程中，将CQVNN分解成4个实值神经网络，通过拓扑度理论、传统的李雅普诺夫稳定性理论以及不等式理论，得到CQVNN平衡点的存在唯一性条件以及其平衡点渐近稳定的充分条件。最后，给出一个数值案例，以验证所得结论的有效性。
Abstract
Because the traditional quaternion multiplication does not meet the commutative law
a kind of commutative quaternion was introduced
and a commutative quaternion valued neural network (CQVNN) was established
and the asymptotic stability of the CQVNN was studied.In the course of research
the CQVNN were decomposed into four real-valued neural networks.Then
through the topological degree theory
the traditional Lyapunov stability theory and the inequality theory
the conditions for the existence and uniqueness of the equilibrium point of CQVNN and the linear matrix inequality (LMI) conditions for the asymptotically stable of equilibrium point were obtained.Finally
a numerical example was given to verify the validity of the conclusion.
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references
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