Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects
Grienggrai Rajchakit, R. Sriraman, N. Boonsatit, Porpattama Hammachukiattikul, Chee Peng Lim, Praveen Agarwal
Abstract
Abstract In this study, we investigate the global exponential stability of Clifford-valued neural network (NN) models with impulsive effects and time-varying delays. By taking impulsive effects into consideration, we firstly establish a Clifford-valued NN model with time-varying delays. The considered model encompasses real-valued, complex-valued, and quaternion-valued NNs as special cases. In order to avoid the issue of non-commutativity of the multiplication of Clifford numbers, we divide the original n -dimensional Clifford-valued 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> -dimensional real-valued models. Then we adopt the Lyapunov–Krasovskii functional and linear matrix inequality techniques to formulate new sufficient conditions pertaining to the global exponential stability of the considered NN model. Through numerical simulation, we show the applicability of the results, along with the associated analysis and discussion.