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Stability Results for Cellular Neural Networks with Time Delays

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Computational Intelligence and Bioinspired Systems (IWANN 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3512))

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Abstract

Cellular neural networks (CNNs) introduced by Chua and Yang in 1988 are recurrent artificial neural networks. Due to their cyclic connections and to the neurons’ nonlinear activation functions, recurrent neural networks are nonlinear dynamic systems, which display stable and unstable fixed points, limit cycles and chaotic behavior. Since the field of neural networks is still a recent one, improving the stability conditions for such systems is an obvious and quasi-permanent task. This paper focuses on CNNs affected by time delays. We are interested to obtain sufficient conditions for the asymptotic stability of a cellular neural network with time delay feedback and zero control templates. Due to their sector restricted nonlinearities, stability of the neural networks is strongly connected to robust stability. With respect to this we shall use a quadratic Liapunov functional constructed via the technique due to V. L. Kharitonov for uncertain linear time delay systems, combined with an approach suggested by Malkin for systems with sector restricted nonlinearities.

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Author information

Authors and Affiliations

  1. Department of Automatic Control, University of Craiova, 13, A.I. Cuza str., 200585, Craiova, Romania

    Daniela Danciu & Vladimir Răsvan

Authors
  1. Daniela Danciu
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  2. Vladimir Răsvan
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Editors and Affiliations

  1. Departamento de Ingeniería Electrónica, Universitat Politècnica de Catalunya (UPC). E.T.S.I. de Telecomunicación, Campus Norte, Edificio C4, C/ Jordi Girona, 1-3, E08034, Barcelona, Spain

    Joan Cabestany

  2. Department of Computer Architecture and Computer Technology, University of Granada,  

    Alberto Prieto

  3. Grupo ISIS, Dpto. Tecnología Electrónica ETSI Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Sandoval

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Danciu, D., Răsvan, V. (2005). Stability Results for Cellular Neural Networks with Time Delays. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_45

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  • DOI: https://doi.org/10.1007/11494669_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26208-4

  • Online ISBN: 978-3-540-32106-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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