Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays

Advances in Difference Equations

article

Rajchakit, G.¹  Sriraman, R.²  Boonsatit, N.³  Hammachukiattikul, P.⁴  Lim, C. P.⁵  Agarwal, P.⁶ 

[1] Department of Mathematics, Faculty of Science, Maejo University;Department of Mathematics, Thiruvalluvar University;Department of Mathematics, Rajamangala University of Technology Suvarnabhumi;Department of Mathematics, Phuket Rajabhat University;Institute for Intelligent Systems Research and Innovation, Deakin University;Department of Mathematics, Anand International College of Engineering

关键词: Clifford-valued neural network;    Exponential stability;    Lyapunov functional;    Lagrange stability;   

DOI  :  10.1186/s13662-021-03415-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper considers the Clifford-valued recurrent neural network (RNN) models, as an augmentation of real-valued, complex-valued, and quaternion-valued neural network models, and investigates their global exponential stability in the Lagrange sense. In order to address the issue of non-commutative multiplication with respect to Clifford numbers, we divide the original n-dimensional Clifford-valued RNN model into$2^{m}n$ real-valued models. On the basis of Lyapunov stability theory and some analytical techniques, several sufficient conditions are obtained for the considered Clifford-valued RNN models to achieve global exponential stability according to the Lagrange sense. Two examples are presented to illustrate the applicability of the main results, along with a discussion on the implications.

【 授权许可】

CC BY