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Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses

Author

Listed:
  • R. Sakthivel

    (Sungkyunkwan University)

  • R. Raja

    (Periyar University)

  • S. M. Anthoni

    (Anna University Coimbatore)

Abstract

In this paper, the problem of stability analysis for a class of delayed stochastic bidirectional associative memory neural network with Markovian jumping parameters and impulses are being investigated. The jumping parameters assumed here are continuous-time, discrete-state homogeneous Markov chain and the delays are time-variant. Some novel criteria for exponential stability in the mean square are obtained by using a Lyapunov function, Ito’s formula and linear matrix inequality optimization approach. The derived conditions are presented in terms of linear matrix inequalities. The estimate of the exponential convergence rate is also given, which depends on the system parameters and impulsive disturbed intension. In addition, a numerical example is given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.

Suggested Citation

  • R. Sakthivel & R. Raja & S. M. Anthoni, 2013. "Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 251-273, July.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:1:d:10.1007_s10957-011-9817-3
    DOI: 10.1007/s10957-011-9817-3
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    References listed on IDEAS

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    1. Song, Qiankun & Wang, Zidong, 2008. "Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3314-3326.
    2. Park, Ju H., 2006. "A novel criterion for global asymptotic stability of BAM neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 446-453.
    3. Lou, Xuyang & Cui, Baotong, 2009. "Stochastic stability analysis for delayed neural networks of neutral type with Markovian jump parameters," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2188-2197.
    4. R. Sakthivel & R. Samidurai & S. M. Anthoni, 2010. "Asymptotic Stability of Stochastic Delayed Recurrent Neural Networks with Impulsive Effects," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 583-596, December.
    5. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
    6. Syed Ali, M. & Balasubramaniam, P., 2009. "Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2191-2199.
    7. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
    8. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 806-818.
    9. Senan, Sibel & Arik, Sabri, 2009. "New results for global robust stability of bidirectional associative memory neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2106-2114.
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