Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks

Author

Qiao, Hong ; Peng, Jigen ; Xu, Zong-Ben

Author_Institution

Dept. of Manuf. Eng. & Eng. Manage., City Univ. of Hong Kong, Kowloon, Hong Kong

Volume

12

Issue

2

fYear

2001

fDate

3/1/2001 12:00:00 AM

Firstpage

360

Lastpage

370

Abstract

In this paper, a new concept called nonlinear measure is introduced to quantify stability of nonlinear systems in the way similar to the matrix measure for stability of linear systems. Based on the new concept, a novel approach for stability analysis of neural networks is developed. With this approach, a series of new sufficient conditions for global and local exponential stability of Hopfield type neural networks is presented, which generalizes those existing results. By means of the introduced nonlinear measure, the exponential convergence rate of the neural networks to stable equilibrium point is estimated, and, for local stability, the attraction region of the stable equilibrium point is characterized. The developed approach can be generalized to stability analysis of other general nonlinear systems

Keywords

Hopfield neural nets; asymptotic stability; convergence; nonlinear systems; Hopfield-type neural networks; exponential convergence rate; exponential stability analysis; global exponential stability; local exponential stability; local stability; nonlinear measures; stable equilibrium point; Associative memory; Convergence; Hopfield neural networks; Linear systems; Lyapunov method; Neural networks; Nonlinear systems; Stability analysis; Sufficient conditions; Transfer functions;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.914530

Filename

914530