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Robust Stability of Uncertain Neural Networks with Time-Varying Delays

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Advances in Neural Networks - ISNN 2008 (ISNN 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5263))

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Abstract

This paper is concerned the robust stability analysis problem for neural networks with time-varying delay and time-varying parametric uncertainties. By utilizing a Lyapunov-Krasovskii functional, we show that the addressed neural networks are robustly, asymptotically stable if a convex optimization problem is feasible. A stability criterion is derived and formulated by means of the feasibility of a linear matrix inequality (LMI), which can be effectively solved by some standard numerical packages. Two numerical examples are given to demonstrate the usefulness of the proposed robust stability criterion.

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References

  1. Wu, H., Mizukami, K.: Robust stability criteria for dynamical systems including delayedperturbations. IEEE Trans. Automat. Control 40, 487–490 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Yan, J., Tsai, J., Kung, F.: A new result on the robust stability of uncertain systems with time-varying delay. IEEE Trans. Circuits and Systems I 48, 914–916 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Xu, B.: A new result on the robust stability on uncertain systems with time-varying delay. Int. J. Syst. Sci. 33, 543–550 (2001)

    Article  Google Scholar 

  4. Zhong, Q.: Robust stability analysis of simple systems controlled over communication networks. Automatica 19, 1309–1312 (2003)

    Google Scholar 

  5. Liu, P., Su, T.: Robust stability of interval time-delay systems with delay-dependence-oscillation. Time Lages. Syst. Control Lett. 33, 231–239 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  6. Jing, X., Tan, D., Wang, Y.: An LMI approach to stability of systems with severe time-delay. IEEE Trans. Automat. Control 49, 1192–1195 (2004)

    Article  MathSciNet  Google Scholar 

  7. Zhang, H., Liao, X.: LMI-based robust stability analysis of neural networks with time-varying delay. Neurocomputing 67, 306–312 (2005)

    Article  Google Scholar 

  8. Singh, V.: LMI approach to the global robust stability of a larger class of neural networks with delay. Chaos, Solitons and Fractals 32, 1927–1934 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Liao, X., Chen, G., Sanchez, E.: LMI-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. Circuits and Systems I 49, 1033–1039 (2002)

    Article  MathSciNet  Google Scholar 

  10. Singh, V.: Robust stability of cellular neural networks with delay: linear matrix inequality approach. IEE Proceedings- Control Theory and Applications 151, 125–129 (2004)

    Article  Google Scholar 

  11. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM, Philadelphia (1994)

    MATH  Google Scholar 

  12. Cao, J.: Global asymptotic stability of neural networks with transmission delays. Int. J. Syst. Sci. 31, 1313–1316 (2000)

    Article  MATH  Google Scholar 

  13. Liao, X., Wong, K., Wu, Z., Chen, G.: Novel robust stability criteria for interval-delayed hopfieldneural networks. IEEE Trans. Circuits and Systems I 48, 1355–1359 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Arik, S.: Global robust stability of delayed neural networks. IEEE Trans. Circuits and Systems I 50, 156–160 (2003)

    Article  MathSciNet  Google Scholar 

  15. Liao, X., Li, C.: An LMI approach to asymptotical stability of multi-delayed neural networks. Physica D 200, 139–155 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Automation, Chongqing University, Chongqing, 40044, China

    Wei Feng

  2. Department of Computer and Modern Education Technology, Chongqing Education College, Chongqing, 400067, China

    Wei Feng, Haixia Wu & Wei Zhang

Authors
  1. Wei Feng
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  2. Haixia Wu
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  3. Wei Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghu University, 100084, Beijing, China

    Fuchun Sun

  2. Institute TAMS (Technical Aspects of Multimodal Systems), department of Informatics, University of Hamburg, Vogt-Koelln-Straße 30, 22527, Hamburg, Germany

    Jianwei Zhang

  3. Intel China Research Center, 8/F, Peking University, Department of Machine Intelligence, 100871, Beijing, China

    Ying Tan

  4. Department of Mathematics, Southeast University, 210096, Nanjing, China

    Jinde Cao

  5. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

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© 2008 Springer-Verlag Berlin Heidelberg

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Feng, W., Wu, H., Zhang, W. (2008). Robust Stability of Uncertain Neural Networks with Time-Varying Delays. In: Sun, F., Zhang, J., Tan, Y., Cao, J., Yu, W. (eds) Advances in Neural Networks - ISNN 2008. ISNN 2008. Lecture Notes in Computer Science, vol 5263. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87732-5_38

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  • DOI: https://doi.org/10.1007/978-3-540-87732-5_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87731-8

  • Online ISBN: 978-3-540-87732-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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