Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

Yanke Du,Rui Xu

doi:10.1155/2012/647231

Abstract

A class of interval neural networks with time‐varying delays and distributed delays is investigated. By employing H‐matrix and M‐matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.

Highlights

In recent years, great attention has been paid to the neural networks due to their applications in many areas such as signal processing, associative memory, pattern recognition, parallel computation, and optimization
Motivated by the works of 15–17 and the discussions above, the purpose of this paper is to present some new sufficient conditions for the global robust exponential stability of neural networks with time-varying and distributed delays
We prove that the unique equilibrium point x∗ is globally robustly exponentially stable

Summary

Introduction

Great attention has been paid to the neural networks due to their applications in many areas such as signal processing, associative memory, pattern recognition, parallel computation, and optimization. In 8 , Zhao and Zhu established some sufficient conditions for the global robust exponential stability for interval neural networks with constant delays. In 18 , Wang et al obtained some criteria for the global robust exponential stability for interval CohenGrossberg neural networks with time-varying delays using LMI, matrix inequality, matrix norm, and Halanay inequality techniques. In 15–17 , employing homeomorphism techniques, Lyapunov method, H-matrix and M-matrix theory, and LMI approach, Shao et al established some sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point for interval Hopfield neural networks with timevarying delays. Motivated by the works of 15–17 and the discussions above, the purpose of this paper is to present some new sufficient conditions for the global robust exponential stability of neural networks with time-varying and distributed delays. A concluding remark is given in Section 5 to end this work

Preliminaries

Global Robust Exponential Stability

Numerical Simulations and Comparisons

Conclusion