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A Novel Criterion for Global Asymptotic Stability of Neutral-Type Neural Networks with Discrete Time Delays

  • Ozlem Faydasicok
  • Sabri Arik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11302)

Abstract

The main target in this work is to propose a new condition for global asymptotic stability for neutral-type neural networks including constant delay parameters. This newly obtained criterion is derived by making the use a properly modified Lyapunov functional with the employment of Lipschitz activation functions, which establishes a new set of relationships among the constant system parameters of this class of neural networks. The obtained condition is expressed independently of delay parameters and can be easily approved by simply checking the validity of some algebraic equations.

Keywords

Discrete time delays Stability theory Neutral-type neural systems Lyapunov theorems 

References

  1. 1.
    Samidurai, S., Marshal, A., Balachandran, R.K.: Global exponential stability of neutral-type impulsive neural networks with discrete and distributed delays. Nonlinear Anal. Hybrid Syst. 4, 103–112 (2010)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Shi, K., Zhu, H., Zhong, S., Zeng, Y., Zhang, Y.: New stability analysis for neutral type neural networks with discrete and distributed delays using a multiple integral approach. J. Franklin Inst. 352, 155–176 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Liao, X., Liu, Y., Wang, H., Huang, T.: Exponential estimates and exponential stability for neutral-type neural networks with multiple delays. Neurocomputing 149, 868–883 (2015)CrossRefGoogle Scholar
  4. 4.
    Arik, S.: An analysis of stability of neutral-type neural systems with constant time delays. J. Franklin Inst. 351, 4949–4959 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Samli, R., Arik, S.: New results for global stability of a class of neutral-type neural systems with time delays. Appl. Math. Comput. 210, 564–570 (2009)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Orman, Z., Arik, S.: An analysis of stability of a class of neutral-type neural networks with discrete time delays. Abstr. Appl. Anal. (2013). Article ID 143585Google Scholar
  7. 7.
    Liu, P.L.: Further improvement on delay-dependent robust stability criteria for neutral-type recurrent neural networks with time-varying delays. ISA Trans. 55, 92–99 (2015)CrossRefGoogle Scholar
  8. 8.
    Zhang, Z., Liu, K., Yang, Y.: New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type. Neurocomputing 81, 24–32 (2012)CrossRefGoogle Scholar
  9. 9.
    Zhang, G., Wang, T., Li, T., Fei, S.: Multiple integral Lyapunov approach to mixed-delay-dependent stability of neutral neural networks. Neurocomputing 275, 1782–1792 (2018)CrossRefGoogle Scholar
  10. 10.
    Shi, K., Zhong, S., Zhu, H., Liu, X., Zeng, Y.: New delay-dependent stability criteria for neutral-type neural networks with mixed random time-varying delays. Neurocomputing 168, 896–90730 (2015)CrossRefGoogle Scholar
  11. 11.
    Wang, B., Liu, X., Zhong, S.: New stability analysis for uncertain neutral system with time-varying delay. Appl. Math. Comput. 197, 457–465 (2008)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zhang, W.A., Yu, L.: Delay-dependent robust stability of neutral systems with mixed delays and nonlinear perturbations. Acta Automat. Sinica 33, 863–866 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Lakshmanan, S., Park, J.H., Jung, H.Y., Kwon, O.M., Rakkiyappan, R.: A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays. Neurocomputing 111, 81–89 (2013)CrossRefGoogle Scholar
  14. 14.
    Lien, C.H., Yu, K.W., Lin, Y.F., Chung, Y.J., Chung, L.Y.: Global exponential stability for uncertain delayed neural networks of neutral type with mixed time delays. IEEE Trans. Syst. Man Cybern. B Cybern. 38, 709–720 (2008)CrossRefGoogle Scholar
  15. 15.
    Akça, H., Covachev, V., Covacheva, Z.: Global asymptotic stability of Cohen-Grossberg neural networks of neutral type. J. Math. Sci. 205, 719–732 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsIstanbul UniversityIstanbulTurkey
  2. 2.Department of Computer EngineeringIstanbul University-CerrahpasaIstanbulTurkey

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