Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/31348
Title: Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis
Authors: Qi, H
Qi, L 
Keywords: Equilibrium point
Generalized Jacobian
Global asymptotic stability (GAS)
Homeomorphism
Invertibility
Lyapunov functions
Neural networks (NNs)
Nonsingularity
Spectral norm
Spectral radius
Issue Date: 2004
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on neural networks, 2004, v. 15, no. 1, p. 99-109 How to cite?
Journal: IEEE transactions on neural networks 
Abstract: In this paper, we obtain new sufficient conditions ensuring existence, uniqueness, and global asymptotic stability (GAS) of the equilibrium point for a general class of delayed neural networks (DNNs) via nonsmooth analysis, which makes full use of the Lipschitz property of functions defining DNNs. Based on this new tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then those results are applied to show that existence assumptions on the equilibrium point in some existing sufficient conditions ensuring GAS are actually unnecessary; and some strong assumptions such as the boundedness of activation functions in some other existing sufficient conditions can be actually dropped. Finally, we derive some new sufficient conditions which are easy to check. Comparison with some related existing results is conducted and advantages are illustrated with examples. Throughout our paper, spectral properties of the matrix (A + Aτ) play an important role, which is a distinguished feature from previous studies. Here, A and Aτ are, respectively, the feedback and the delayed feedback matrix defining the neural network under consideration.
URI: http://hdl.handle.net/10397/31348
ISSN: 1045-9227
DOI: 10.1109/TNN.2003.820836
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