Exponential stability in the Lagrange sense for Clifford-valued recurrent neural networks with time delays
Grienggrai Rajchakit, R. Sriraman, N. Boonsatit, Porpattama Hammachukiattikul, Chee Peng Lim, Praveen Agarwal
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 $2^{m}n$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msup><mml:mi>n</mml:mi></mml:math> 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.