Necessary and Sufficient Condition for Absolute Exponential Stability of a Class of Nonsymmetric Neural Networks
Summary :
In this paper, we prove that for a class of nonsymmetric neural networks with connection matrices T having nonnegative off-diagonal entries, -T is an M-matrix is a necessary and sufficient condition for absolute exponential stability of the network belonging to this class. While this result extends the existing one of absolute stability in Forti, et al., its proof given in this paper is simpler, which is completed by an approach different from one used in Forti, et al. The most significant consequence is that the class of nonsymmetric neural networks with connection matrices T satisfying -T is an M-matrix is the largest class of nonsymmetric neural networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses. An illustrating numerical example is also given.
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- IEICE TRANSACTIONS on Information Vol.E80-D No.8 pp.802-807
- Publication Date
- 1997/08/25
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- Bio-Cybernetics and Neurocomputing
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Xue-Bin LIANG, Toru YAMAGUCHI, "Necessary and Sufficient Condition for Absolute Exponential Stability of a Class of Nonsymmetric Neural Networks" in IEICE TRANSACTIONS on Information,
vol. E80-D, no. 8, pp. 802-807, August 1997, doi: .
Abstract: In this paper, we prove that for a class of nonsymmetric neural networks with connection matrices T having nonnegative off-diagonal entries, -T is an M-matrix is a necessary and sufficient condition for absolute exponential stability of the network belonging to this class. While this result extends the existing one of absolute stability in Forti, et al., its proof given in this paper is simpler, which is completed by an approach different from one used in Forti, et al. The most significant consequence is that the class of nonsymmetric neural networks with connection matrices T satisfying -T is an M-matrix is the largest class of nonsymmetric neural networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses. An illustrating numerical example is also given.
URL: https://global.ieice.org/en_transactions/information/10.1587/e80-d_8_802/_p
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@ARTICLE{e80-d_8_802,
author={Xue-Bin LIANG, Toru YAMAGUCHI, },
journal={IEICE TRANSACTIONS on Information},
title={Necessary and Sufficient Condition for Absolute Exponential Stability of a Class of Nonsymmetric Neural Networks},
year={1997},
volume={E80-D},
number={8},
pages={802-807},
abstract={In this paper, we prove that for a class of nonsymmetric neural networks with connection matrices T having nonnegative off-diagonal entries, -T is an M-matrix is a necessary and sufficient condition for absolute exponential stability of the network belonging to this class. While this result extends the existing one of absolute stability in Forti, et al., its proof given in this paper is simpler, which is completed by an approach different from one used in Forti, et al. The most significant consequence is that the class of nonsymmetric neural networks with connection matrices T satisfying -T is an M-matrix is the largest class of nonsymmetric neural networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses. An illustrating numerical example is also given.},
keywords={},
doi={},
ISSN={},
month={August},}
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TY - JOUR
TI - Necessary and Sufficient Condition for Absolute Exponential Stability of a Class of Nonsymmetric Neural Networks
T2 - IEICE TRANSACTIONS on Information
SP - 802
EP - 807
AU - Xue-Bin LIANG
AU - Toru YAMAGUCHI
PY - 1997
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E80-D
IS - 8
JA - IEICE TRANSACTIONS on Information
Y1 - August 1997
AB - In this paper, we prove that for a class of nonsymmetric neural networks with connection matrices T having nonnegative off-diagonal entries, -T is an M-matrix is a necessary and sufficient condition for absolute exponential stability of the network belonging to this class. While this result extends the existing one of absolute stability in Forti, et al., its proof given in this paper is simpler, which is completed by an approach different from one used in Forti, et al. The most significant consequence is that the class of nonsymmetric neural networks with connection matrices T satisfying -T is an M-matrix is the largest class of nonsymmetric neural networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses. An illustrating numerical example is also given.
ER -
English
