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Stochastic Robust Stability of Markovian Jump Nonlinear Uncertain Neural Networks with Wiener Process

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Book cover Advances in Neural Networks - ISNN 2006 (ISNN 2006)

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Abstract

This paper deals with the stochastic robust stability problem for Markovian jump nonlinear uncertain neural networks (MJNUNNs) with Wiener process. Some criteria for stochastic robust stability of Markovian jump nonlinear uncertain neural networks are derived, even if the system contains Wiener process. All the derived results are presented in terms of linear matrix inequality.

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References

  1. Rong, L.B.: LMI Approach for Global Periodicity of Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Systems I: Regular Papers 52(7), 1451–1458 (2005)

    Article  MathSciNet  Google Scholar 

  2. Cao, J., Liang, J.: Boundedness and Stability for Cohen-Grossberg Neural Network with Time-Varying Delays. J. Math. Anal. Appl. 296(2), 665–685 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Lu, H.T.: Absolute Exponential Stability Analysis of Delayed Neural Networks. Physics Letters A 336(2-3), 133–140 (2005)

    Article  MATH  Google Scholar 

  4. Lu, H.T., He, Z.Y.: Global Exponential Stability of Delayed Competitive Neural Networks with Different Time Scales. Neural Networks 18(3), 243–250 (2005)

    Article  MATH  Google Scholar 

  5. Cao, J.D., Huang, D.S., Qu, Y.Z.: Global Robust Stability of Delayed Recurrent Neural Networks. Chaos, Solitons and Fractals 23(1), 221–229 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cao, J.D., Chen, T.P.: Globally Exponentially Robust Stability and Periodicity of Delayed Neural Networks. Chaos, Solitons and Fractals 22(4), 957–963 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Lou, X.Y., Cui, B.T.: Global Asymptotic Stability of BAM Neural Networks with Distributed Delays and Reaction-Diffusion Terms. Chaos, Solitons and Fractals 27(5), 1347–1354 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  8. Huang, X., Cao, J.D., Huang, D.S.: LMI-Based Approach for Delay-dependent Exponential Stability Analysis of BAM Neural Networks. Chaos, Solitons and Fractals 24(3), 885–898 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cao, J.D.: On Exponential Stability and Periodic Solutions of CNNs with Delays. Phys. Lett. A 267(5-6), 312–318 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Cao, J.D., Zhou, D.M.: Stability Analysis of Delayed Cellular Neural Networks. Neural Networks 11(9), 1601–1605 (1998)

    Article  Google Scholar 

  11. Cao, J.D., Jiang, Q.H.: An Analysis of Periodic Solutions of Bi-Directional Associative Memory Networks with Time-Varying Delays. Physics Letters A 330(3-4), 203–213 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Liang, J.L., Cao, J.D., Ho, D.W.C.: Discrete-Time Bidirectional Associative Memory Neural Networks with Variable Delays. Physics Letters A 335(2-3), 226–234 (2005)

    Article  MATH  Google Scholar 

  13. Li, C.D., Liao, X.F., Zhang, R.: Delay-Dependent Exponential Stability Analysis of Bi-Directional Associative Memory Neural Networks with Time Delay: an LMI Approach. Chaos, Solitons and Fractals 24(4), 1119–1134 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mao, X.R.: Stochastic Differential Equations and Applications. Horwood, Chichester (1997)

    Google Scholar 

  15. Liao, X.X., Mao, X.R.: Exponential Stability and Instability of Stochastic Neural Networks. Stochast. Anal. Appl. 14(2), 165–185 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  16. Wan, L., Sun, J.H.: Mean Square Exponential Stability of Stochastic Delayed Hopfield Neural Networks. Physics Letters A 343(4), 306–318 (2005)

    Article  MATH  Google Scholar 

  17. Huang, H., Ho, D.W.C., Lam, J.: Stochastic Stability Analysis of Fuzzy Hopfield Neural Networks with Time-Varying Delays. IEEE Trans. Circuits Systems II: Express Briefs 52(5), 251–255 (2005)

    Article  Google Scholar 

  18. Xie, L.: Stochastic Robust Stability Analysis for Markovian Jumping Neural Networks with Time Delays. In: The 2005 IEEE International Conference on Networking, Sensing and Control, pp. 923–928 (2005)

    Google Scholar 

  19. Liao, X.X., Mao, X.R.: Stability of Stochastic Neural Networks. Neural, Para. Sci. Comput. 4(2), 205–224 (1996)

    MATH  MathSciNet  Google Scholar 

  20. Blythe, S., Mao, X.R., Shah, A.: Razumikhin-Type Theorems on Stability of Stochastic Neural Networks with Delays. Stochast. Anal. Appl. 19(1), 85–101 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  21. Amold, L.: Stochastic Differential Equations: Theory and Applications. Loh Wilry and Sons, New York (1974)

    Google Scholar 

  22. Boukas, E.K., Liu, K.: Deterministic and Stochastic Systems with Time-Delay. Birkhauser, Boston (2002)

    Google Scholar 

  23. Raouf, J., Boukas, E.K.: Robust Stabilization of Markovian Jump Linear Singular Systems with Wiener Process. In: Proc. of the 2004 American Control Conference, pp. 3170–3175. Boston, Massachusetts (2004)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Lou, X., Cui, B. (2006). Stochastic Robust Stability of Markovian Jump Nonlinear Uncertain Neural Networks with Wiener Process. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_25

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  • DOI: https://doi.org/10.1007/11759966_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34439-1

  • Online ISBN: 978-3-540-34440-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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