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

Abstract

Abstract 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 $2^{m}n$ 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.

Keywords

• Clifford-valued neural network
• Exponential stability
• Lyapunov functional
• Lagrange stability