Absolutely exponential stability of a class of neural networks with unbounded delay

Authors:
Jiye Zhang;Yoshihiro Suda;Takashi Iwasa
Affiliations:
National Traction Power Laboratory, Southwest Jiaotong University, Chengdu 610031, China and Center for Collaborative Research, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Ja ...;Center for Collaborative Research, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan;Center for Collaborative Research, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
Venue:
Neural Networks
Year:
2004

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Abstract

In this paper, the existence and uniqueness of the equilibrium point and absolute stability of a class of neural networks with partially Lipschitz continuous activation functions are investigated. The neural networks contain both variable and unbounded delays. Using the matrix property, a necessary and sufficient condition for the existence and uniqueness of the equilibrium point of the neural networks is obtained. By constructing proper vector Liapunov functions and nonlinear integro-differential inequalities involving both variable delays and unbounded delay, using M-matrix theory, sufficient conditions for absolutely exponential stability are obtained.