Global exponential stability of Clifford-valued neural networks with time-varying delays and impulsive effects

G Rajchakit,R Sriraman,P Hammachukiattikul,N Boonsatit,P Agarwal,C P Lim

doi:10.1186/s13662-021-03367-z

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-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.

Highlights

Dynamic analysis of neural network (NN) models has gained tremendous research interest in recent decades, since NN models play a significant role in various applications
Motivated by the above facts, our research focuses on to derive the sufficient conditions of global exponential stability of Clifford-valued NNs with impulsive effects
The main contributions of our study are as follows: (1) we for the first time analyze the global exponential stability of Clifford-valued NN models with time-varying delays as well as impulsive effects; (2) in comparison with other results, the results of our study is new and more general even when the considered Clifford-valued NN model has been decomposed into real, complex, and quaternion-valued NN models; (3) our proposed method can be employed for other dynamic behaviors with respect to different types of Clifford-valued NN models

Summary

Introduction

Dynamic analysis of neural network (NN) models has gained tremendous research interest in recent decades, since NN models play a significant role in various applications. To the best of our knowledge, there are hardly any papers that deal with the issue of global exponential stability of Clifford-valued NNs with time-varying delays and impulsive effects. The main contributions of our study are as follows: (1) we for the first time analyze the global exponential stability of Clifford-valued NN models with time-varying delays as well as impulsive effects; (2) in comparison with other results, the results of our study is new and more general even when the considered Clifford-valued NN model has been decomposed into real-, complex-, and quaternion-valued NN models; (3) our proposed method can be employed for other dynamic behaviors with respect to different types of Clifford-valued NN models.

Notations

Clifford Algebra The Clifford real algebra over Rm is defined as

Main results

Exponential stability

Conclusion