Globally Exponential Stability and Globally Power Stability of Quaternion-Valued Neural Networks With Discrete and Distributed Delays

Huiling Duan,Tao Peng,Jianlong Qiu,Zhengwen Tu,Jianquan Lu

doi:10.1109/access.2020.2978647

Abstract

This paper investigates the stability of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed delays. By decomposing the QVNN and forming an equivalent real-valued vector-matrix differential equation (RVVDE), based on the Lyapunov theory and some matrix inequalities, some sufficient conditions are derived to ensure the existence and uniqueness, the globally exponential stability and the globally power stability of the equilibrium of RVVDE. These conditions also apply to the QVNN. Two numerical examples are given to show the advantage and the effectiveness of the main results.

Highlights

Neural network is a parallel distributed processor with a large number of connections, and it has an adaptive ability to acquire knowledge through learning [1]
Enlightened by the above analysis, this paper investigates the stability problem of a class of quaternion-valued neural networks (QVNNs) with discrete and distributed delays, by decomposing the QVNN into four real-valued neural networks and forming a real-valued vector-matrix differential equation (RVVDE)
Without too many restrictions compared with Theorem 1 in [23], are suitable for QVNNs and for real-valued neural networks (RVNNs)

Summary

INTRODUCTION

Neural network is a parallel distributed processor with a large number of connections, and it has an adaptive ability to acquire knowledge through learning [1]. Many interesting results on the stability of the equilibrium point of the real-valued neural networks (RVNNs), whose state variables, activation functions, link. Enlightened by the above analysis, this paper investigates the stability problem of a class of QVNNs with discrete and distributed delays, by decomposing the QVNN into four real-valued neural networks and forming a RVVDE. By constructing some new Lyapunov–Krasovskii functionals and matrix inequalities, three sufficient conditions are proposed to ensure the existence and uniqueness, the globally exponential stability and the globally power stability of the equilibrium of the RVVDE Note that these criteria, without too many restrictions compared with Theorem 1 in [23], are suitable for QVNNs and for RVNNs. our criteria formulated by matrix inequalities can be checked, and our decomposition methods are of faster convergence speed than the results in [27].

H11 H12 H1T2 H22

ILLUSTRATIVE EXAMPLES

CONCLUSION