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

• Published in: Advances in difference equations Vol. 2021; no. 1; pp. 1 - 21
• Main Authors: Rajchakit, G., Sriraman, R., Boonsatit, N., Hammachukiattikul, P., Lim, C. P., Agarwal, P.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 17-05-2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Clifford-valued neural network; Difference and Functional Equations; Exponential stability; Functional Analysis; Lagrange stability; Lyapunov functional; Mathematics; Mathematics and Statistics; Multiplication; Neural networks; Ordinary Differential Equations; Partial Differential Equations; Quaternions; Recurrent neural networks; Stability analysis; Clifford-valued neural network; Lyapunov functional; Exponential stability; Lagrange stability
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-021-03415-8

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.