article

A new approach to stability of neural networks with time-varying delays

Authors:

Zong-ben XuAuthors Info & Claims

Neural Networks, Volume 15, Issue 1

Pages 95 - 103

https://doi.org/10.1016/S0893-6080(01)00095-8

Published: 01 January 2002 Publication History

Abstract

The stability of neural networks is a prerequisite for successful applications of the networks as either associative memories or optimization solvers. Because the integration and communication delays are ubiquitous, the stability of neural networks with delays has received extensive attention. However, the approach used in the previous investigation is mainly based on Liapunov's direct method. Since the construction of Liapunov function is very skilful, there is little compatibility among the existing results. In this paper, we develop a new approach to stability analysis of Hopfield-type neural networks with time-varying delays by defining two novel quantities of nonlinear function similar to the matrix norm and the matrix measure, respectively. With the new approach, we present sufficient conditions of the stabliity, which are either the generalization of those existing or new. The developed approach may be also applied for any general system with time delays rather than Hopfield-type neural networks.

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Cited By

Si WWang NYang C(2021)Composite dynamic movement primitives based on neural networks for human–robot skill transferNeural Computing and Applications10.1007/s00521-021-05747-835:32(23283-23293)Online publication date: 13-Feb-2021
https://dl.acm.org/doi/10.1007/s00521-021-05747-8
Arbi AAouiti CChérif FTouati AAlimi A(2015)Stability analysis for delayed high-order type of Hopfield neural networks with impulsesNeurocomputing10.1016/j.neucom.2015.03.021165:C(312-329)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1016/j.neucom.2015.03.021
Arbi AAouiti CChérif FTouati AAlimi A(2015)Stability analysis of delayed Hopfield Neural Networks with impulses via inequality techniquesNeurocomputing10.1016/j.neucom.2014.10.036158:C(281-294)Online publication date: 22-Jun-2015
https://dl.acm.org/doi/10.1016/j.neucom.2014.10.036
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Index Terms

A new approach to stability of neural networks with time-varying delays
1. Computing methodologies
2. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computations on matrices

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cover image Neural Networks

Neural Networks Volume 15, Issue 1

January 2002

142 pages

ISSN:0893-6080

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Publisher

Elsevier Science Ltd.

United Kingdom

Publication History

Published: 01 January 2002

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Cited By

Si WWang NYang C(2021)Composite dynamic movement primitives based on neural networks for human–robot skill transferNeural Computing and Applications10.1007/s00521-021-05747-835:32(23283-23293)Online publication date: 13-Feb-2021
https://dl.acm.org/doi/10.1007/s00521-021-05747-8
Arbi AAouiti CChérif FTouati AAlimi A(2015)Stability analysis for delayed high-order type of Hopfield neural networks with impulsesNeurocomputing10.1016/j.neucom.2015.03.021165:C(312-329)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1016/j.neucom.2015.03.021
Arbi AAouiti CChérif FTouati AAlimi A(2015)Stability analysis of delayed Hopfield Neural Networks with impulses via inequality techniquesNeurocomputing10.1016/j.neucom.2014.10.036158:C(281-294)Online publication date: 22-Jun-2015
https://dl.acm.org/doi/10.1016/j.neucom.2014.10.036
Xueli SJigen P(2011)A novel approach to exponential stability of nonlinear systems with time-varying delaysJournal of Computational and Applied Mathematics10.1016/j.cam.2010.09.011235:6(1700-1705)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1016/j.cam.2010.09.011
Hu CJiang HTeng Z(2010)Globally Exponential Stability for Delayed Neural Networks Under Impulsive ControlNeural Processing Letters10.1007/s11063-009-9128-y31:2(105-127)Online publication date: 1-Apr-2010
https://dl.acm.org/doi/10.1007/s11063-009-9128-y
Jiang HTeng Z(2009)Boundedness, periodic solutions and global stability for cellular neural networks with variable coefficients and infinite delaysNeurocomputing10.1016/j.neucom.2008.11.01072:10-12(2455-2463)Online publication date: 1-Jun-2009
https://dl.acm.org/doi/10.1016/j.neucom.2008.11.010
Xu BLiu XTeo K(2009)Global exponential stability of impulsive high-order Hopfield type neural networks with delaysComputers & Mathematics with Applications10.1016/j.camwa.2008.10.00157:11-12(1959-1967)Online publication date: 1-Jun-2009
https://dl.acm.org/doi/10.1016/j.camwa.2008.10.001
Wan AMao WQiao HZhang B(2009)Global Asymptotic Stability of Cohen-Grossberg Neural Networks with Multiple Discrete DelaysProceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence10.1007/978-3-540-74205-0_6(47-58)Online publication date: 17-Nov-2009
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Parizangeneh MAtaei MMoallem P(2008)Embedding dimension estimation of high dimensional chaotic time series using distributed time delay neural networkProceedings of the 8th conference on Systems theory and scientific computation10.5555/1503773.1503821(284-290)Online publication date: 20-Aug-2008
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Wan AMao W(2008)Criteria for Exponential Stability of Cohen-Grossberg Neural Networks with Multiple Time-Varying DelaysProceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Artificial Intelligence10.1007/978-3-540-85984-0_3(19-26)Online publication date: 15-Sep-2008
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