Stability analysis of delayed cellular neural networks described using cloning templates

We show that any N/spl times/M-dimensional delayed cellular neural network described using cloning templates can have no more than 3/sup N/spl times/M/ isolated equilibrium points and 2/sup N/spl times/M/ of these equilibrium points located in saturation regions are locally exponentially stable. In...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 2004-11, Vol.51 (11), p.2313-2324
Main Authors: Zeng, Z., Wang, J., Liao, X.
Format: Article
Language:English
Subjects:
Array signal processing
Automation
Cellular neural network (CNN)
Cellular neural networks
Cloning
cloning template
Computer networks
Delay
Image processing
isolated equilibria
Large-scale systems
Neural networks
stability
Stability analysis
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Summary:We show that any N/spl times/M-dimensional delayed cellular neural network described using cloning templates can have no more than 3/sup N/spl times/M/ isolated equilibrium points and 2/sup N/spl times/M/ of these equilibrium points located in saturation regions are locally exponentially stable. In addition, we give the conditions for the equilibrium points to be locally exponentially stable when the equilibrium points locate the designated saturation region. These conditions improve and extend the existing stability results in the literature. The conditions are also very easy to be verified and can be checked by direct examination of the templates, regardless of the number of cells. Finally, the validity and performance of the results are illustrated by use of two numerical examples.
ISSN:1549-8328
1057-7122
1558-0806
DOI:10.1109/TCSI.2004.836855