On the complete stability of nonsymmetric cellular neural networks

Norikazu Takahashi; Leon O. Chua

doi:10.1109/81.703843

On the complete stability of nonsymmetric cellular neural networks

Norikazu Takahashi, Leon O. Chua

Research output: Contribution to journal › Article › peer-review

62 Citations (Scopus)

Abstract

This paper gives a new sufficient condition for complete stability of a nonsymmetric cellular neural network (CNN). The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in our proof. It is also shown that the existence of a stable equilibrium point does not imply complete stability of a nonsymmetric CNN.

Original language	English
Pages (from-to)	754-758
Number of pages	5
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	45
Issue number	7
DOIs	https://doi.org/10.1109/81.703843
Publication status	Published - 1998
Externally published	Yes

Keywords

Cellular neural networks
Complete stability
Gaussseidel method

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/81.703843

Cite this

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title = "On the complete stability of nonsymmetric cellular neural networks",

abstract = "This paper gives a new sufficient condition for complete stability of a nonsymmetric cellular neural network (CNN). The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in our proof. It is also shown that the existence of a stable equilibrium point does not imply complete stability of a nonsymmetric CNN.",

keywords = "Cellular neural networks, Complete stability, Gaussseidel method",

author = "Norikazu Takahashi and Chua, {Leon O.}",

note = "Funding Information: Manuscript rceived April 12, 1997; revised October 20, 1997. This work was supported by a Grant-In-Aid from Kyushu Industrial Technology Center, Japan. This paper was recommended by Associate Editor J. Pineda-de-Gyvez. N. Takahashi is with the Department of Informatics, Kyushu University, Kasuga 816-8580, Japan. L. O. Chua is with the Electronics Research Laboratory and Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720 USA. Publisher Item Identifier S 1057-7122(98)05308-2.",

year = "1998",

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AU - Takahashi, Norikazu

AU - Chua, Leon O.

N1 - Funding Information: Manuscript rceived April 12, 1997; revised October 20, 1997. This work was supported by a Grant-In-Aid from Kyushu Industrial Technology Center, Japan. This paper was recommended by Associate Editor J. Pineda-de-Gyvez. N. Takahashi is with the Department of Informatics, Kyushu University, Kasuga 816-8580, Japan. L. O. Chua is with the Electronics Research Laboratory and Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720 USA. Publisher Item Identifier S 1057-7122(98)05308-2.

PY - 1998

Y1 - 1998

N2 - This paper gives a new sufficient condition for complete stability of a nonsymmetric cellular neural network (CNN). The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in our proof. It is also shown that the existence of a stable equilibrium point does not imply complete stability of a nonsymmetric CNN.

AB - This paper gives a new sufficient condition for complete stability of a nonsymmetric cellular neural network (CNN). The convergence theorem of the Gauss-Seidel method, which is an iterative technique for solving a linear algebraic equation, plays an important role in our proof. It is also shown that the existence of a stable equilibrium point does not imply complete stability of a nonsymmetric CNN.

KW - Cellular neural networks

KW - Complete stability

KW - Gaussseidel method

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On the complete stability of nonsymmetric cellular neural networks

Abstract

Keywords

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