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Robust Exponential Stability Criteria for T–S Fuzzy Stochastic Delayed Neural Networks of Neutral Type

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Abstract

This paper is concerned with the problem of robust exponential stability for T–S fuzzy stochastic neural networks of neutral type. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, new delay-dependent stability criteria are established in terms of linear matrix inequalities (LMIs) which can be checked easily by the LMI Control Toolbox in MATLAB. Finally, numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.

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References

  1. S. Arik, An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Netw. 13, 1239–1242 (2002)

    Article  Google Scholar 

  2. B. Boyd, L.E. Ghoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)

    MATH  Google Scholar 

  3. Y.Y. Cao, P.M. Frank, Analysis and synthesis of nonlinear time delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst. 8, 200–211 (2000)

    Article  Google Scholar 

  4. Y.Y. Cao, P.M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. IEEE Trans. Fuzzy Syst. 124, 213–229 (2001)

    MathSciNet  MATH  Google Scholar 

  5. W. Chen, X. Lu, Mean square exponential stability of uncertain stochastic delayed neural networks. Phys. Lett. A 372, 1061–1069 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Chen, Y. Zhang, P. Hu, Novel delay-dependent robust stability criteria for neutral stochastic delayed neural networks. Neurocomputing 73, 2554–2561 (2010)

    Article  Google Scholar 

  7. W. Feng, S.X. Yang, H. Wu, On robust stability of uncertain stochastic neural networks with distributed and interval time-varying delays. Chaos Solitons Fractals 42, 2095–2104 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. K. Gu, Integral inequality in the stability problem of Time-Delay Systems, in Proceeding 39th IEEE CDC, Sydney, Philadelphia (1994)

    Google Scholar 

  9. S. Haykin, Neural Networks: A Comprehensive Foundation (Prentice Hall, New York, 1998)

    Google Scholar 

  10. M. Hua, F. Deng, X. Liu, Y. Peng, Robust delay-dependent exponential stability of uncertain stochastic system with time-varying delay. Circuits Syst. Signal Process. 29, 515–526 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Hua, X. Liu, F. Deng, J. Fei, New results on robust exponential stability of uncertain stochastic neural networks with mixed time-varying delays. Neural Process. Lett. (2010) doi:10.1007/s11063-010-9152-y

    Google Scholar 

  12. H. Huang, D.W.C. Ho, J. Lam, Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delay. IEEE Trans. Circuits Syst. II 52, 251–255 (2005)

    Article  Google Scholar 

  13. T. Huang, Exponential stability of fuzzy cellular neural networks with distributed delay. Phys. Lett. A 351, 48–52 (2006)

    Article  MATH  Google Scholar 

  14. O.M. Kwon, S.M. Lee, J.H. Park, Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays. Phys. Lett. A 374, 1232–1241 (2010)

    Article  MathSciNet  Google Scholar 

  15. X. Li, Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects. Neurocomputing 73, 749–758 (2010)

    Article  Google Scholar 

  16. X. Li, Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Appl. Math. Comput. 215, 4370–4384 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. Liu, W. Tang, Exponential stability of fuzzy cellular neural networks with constant and time-varying delays. Phys. Lett. A 323, 224–233 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Y.R. Liu, Z.D. Wang, X. Liu, Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19, 667–675 (2006)

    Article  MATH  Google Scholar 

  19. T. Li, L. Guob, C. Suna, Further results on asymptotic stability criterion of neural networks with time-varying delays. Neurocomputing 71, 439–447 (2007)

    Article  Google Scholar 

  20. H. Li, B. Chen, C. Lin, Q. Zhou, Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays. Neurocomputing 72, 2017–2023 (2009)

    Article  Google Scholar 

  21. L. Ma, F. Da, Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays. Phys. Lett. A 373, 2154–2161 (2009)

    Article  MathSciNet  Google Scholar 

  22. M.S. Mahmoud, A. Ismail, Improved results on robust exponential stability criteria for neutral-type delayed neural networks. Appl. Math. Comput. 217, 3011–3019 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Mai, X. Liao, C. Li, A semi-free weighting matrices approach for neutral-type delayed neural networks. J. Comput. Appl. Math. 225, 44–55 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. J.H. Park, O.M. Kwon, Global stability for neural networks of neutral-type with interval time-varying delays. Chaos Solitons Fractals 41, 1174–1181 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. R. Raja, R. Sakthivel, S.M. Anthoni, Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects. Can. J. Phys. 88, 885–898 (2010)

    Article  Google Scholar 

  26. R. Rakkiyappan, P. Balasubramaniam, LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl. Math. Comput. 204, 317–324 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Rakkiyappan, P. Balasubramaniam, Delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with mixed time-varying delays: an LMI approach. Nonlinear Anal. Hybrid Syst 4, 600–607 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. R. Sakthivel, R. Samidurai, S.M. Anthoni, New exponential stability criteria for stochastic BAM neural networks with impulses. Phys. Scr. 82, 045802 (2010)

    Article  Google Scholar 

  29. R. Sakthivel, R. Samidurai, S.M. Anthoni, Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects. J. Optim. Theory Appl. 147, 583–596 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Sakthivel, R. Samidurai, S.M. Anthoni, Exponential stability for stochastic neural networks of neutral type with impulsive effects. Mod. Phys. Lett. B 24, 1099–1110 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. H. Shao, Novel delay-dependent stability results for neural networks with time-varying delays. Circuits Syst. Signal Process. 29, 637–647 (2010)

    Article  MATH  Google Scholar 

  32. L. Sheng, M. Gao, H. Yang, Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time-varying delays. Fuzzy Sets Syst. 160, 3503–3517 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  33. W. Su, Y. Chen, Global asymptotic stability analysis for neutral stochastic neural networks with time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 14, 1576–1581 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. M. Syed Ali, P. Balasubramaniam, S. Arik, Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays. Expert Syst. Appl. 14, 2776–2783 (2010)

    Google Scholar 

  35. T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985)

    MATH  Google Scholar 

  36. J. Yu, K. Zhang, S. Fei, Further results on mean square exponential stability of uncertain stochastic delayed neural networks. Commun. Nonlinear Sci. Numer. Simul. 14, 1582–1589 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. Q. Zhang, X. Wei, J. Xu, Delay-dependent global stability condition for delayed Hopfield neural networks. Nonlinear Anal., Real World Appl. 8, 997–1002 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Q. Zhu, J. Cao, Stability analysis for stochastic neural networks of neutral type with both Markovian jump parameters and mixed time delays. Neurocomputing 73, 2671–2680 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Madurai Kamaraj University, Madurai, 625 021, Tamilnadu, India

    S. Muralisankar & N. Gopalakrishnan

  2. Department of Mathematics, Gandhigram Rural University, Gandhigram, 624 302, Tamilnadu, India

    P. Balasubramaniam

Authors
  1. S. Muralisankar
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  2. N. Gopalakrishnan
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  3. P. Balasubramaniam
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Correspondence to S. Muralisankar.

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Muralisankar, S., Gopalakrishnan, N. & Balasubramaniam, P. Robust Exponential Stability Criteria for T–S Fuzzy Stochastic Delayed Neural Networks of Neutral Type. Circuits Syst Signal Process 30, 1617–1641 (2011). https://doi.org/10.1007/s00034-011-9283-z

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  • DOI: https://doi.org/10.1007/s00034-011-9283-z

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