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Asymptotic Stability of Stochastic Delayed Recurrent Neural Networks with Impulsive Effects

Author

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  • R. Sakthivel

    (Sungkyunkwan University)

  • R. Samidurai

    (Periyar University)

  • S. M. Anthoni

    (Anna University Coimbatore)

Abstract

In this paper, the asymptotic stability for a class of stochastic neural networks with time-varying delays and impulsive effects are considered. By employing the Lyapunov functional method, combined with linear matrix inequality optimization approach, a new set of sufficient conditions are derived for the asymptotic stability of stochastic delayed recurrent neural networks with impulses. A numerical example is given to show that the proposed result significantly improve the allowable upper bounds of delays over some existing results in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:3:d:10.1007_s10957-010-9728-8
    DOI: 10.1007/s10957-010-9728-8
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    References listed on IDEAS

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    1. V. N. Phat & Q. P. Ha, 2009. "H ∞ Control and Exponential Stability of Nonlinear Nonautonomous Systems with Time-Varying Delay," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 603-618, September.
    2. Rakkiyappan, R. & Balasubramaniam, P., 2009. "LMI conditions for stability of stochastic recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1688-1696.
    3. Huang, He & Feng, Gang, 2007. "Delay-dependent stability for uncertain stochastic neural networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 93-103.
    4. Zhu, Wenli & Hu, Jin, 2006. "Stability analysis of stochastic delayed cellular neural networks by LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 171-174.
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    Cited by:

    1. 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.
    2. Samidurai, Rajendran & Manivannan, Raman, 2015. "Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 743-762.
    3. R. Sakthivel & R. Raja & S. M. Anthoni, 2011. "Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 166-187, July.
    4. Ren, Yong & He, Qian & Gu, Yuanfang & Sakthivel, R., 2018. "Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 56-66.

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