Robust stability analysis of quaternion-valued neural networks via LMI approach

Xiaofeng Chen,Zhongshan Li,Lianjie Li

doi:10.1186/s13662-018-1585-z

Abstract

This paper is concerned with the issue of robust stability for quaternion-valued neural networks (QVNNs) with leakage, discrete and distributed delays by employing a linear matrix inequality (LMI) approach. Based on the homeomorphic mapping theorem, the quaternion matrix theorem and the Lyapunov theorem, some criteria are developed in the form of real-valued LMIs for guaranteeing the existence, uniqueness, and global robust stability of the equilibrium point of the delayed QVNNs. Two numerical examples are provided to demonstrate the effectiveness of the obtained results.

Highlights

The quaternions are members of a noncommutative division algebra invented independently by Carl Friedrich Gauss in 1819 and William Rowan Hamilton in 1843 [1]
An increasing number of applications based on quaternions are found in various fields, such as computer graphics, quantum mechanics, attitude control, signal processing, and orbital mechanics [3,4,5]
We further consider the global robust stability of the equilibrium point based on Theorem 1

Summary

Introduction

The quaternions are members of a noncommutative division algebra invented independently by Carl Friedrich Gauss in 1819 and William Rowan Hamilton in 1843 [1]. In [32, 33], some μstability criteria in the form of linear matrix inequalities (LMIs) were provided for QVNNs with time-varying delays. In [35], several sufficient criteria were derived to ensure the existence, uniqueness, and global robust stability of the equilibrium point for delayed QVNNs with parameter uncertainties.

Results

Conclusion