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Delay-dependent stability for uncertain stochastic neural networks with time-varying delay

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  • Huang, He
  • Feng, Gang

Abstract

This paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with time-varying delay. The parameter uncertainties are assumed to be norm bounded. By defining a new Lyapunov–Krasovskii functional, the restrictions such as the time-varying delay was required to be differentiable and its derivative was strictly smaller than one, are removed. Based on the linear matrix inequality approach, delay-dependent stability criteria are obtained such that for all admissible uncertainties, the stochastic neural network is globally asymptotically stable in the mean square. Two slack variables are introduced into the obtained stability criteria to reduce the conservatism. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:93-103
    DOI: 10.1016/j.physa.2007.04.020
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    References listed on IDEAS

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    1. Zhang, Hongbin & Li, Chunguang & Liao, Xiaofeng, 2005. "A note on the robust stability of neural networks with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 357-360.
    2. Wang, Zidong & Lauria, Stanislao & Fang, Jian’an & Liu, Xiaohui, 2007. "Exponential stability of uncertain stochastic neural networks with mixed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 62-72.
    3. Cao, Jinde & Ho, Daniel W.C., 2005. "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1317-1329.
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    Cited by:

    1. Pharunyou Chanthorn & Grienggrai Rajchakit & Jenjira Thipcha & Chanikan Emharuethai & Ramalingam Sriraman & Chee Peng Lim & Raja Ramachandran, 2020. "Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    2. 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.
    3. 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.
    4. Feng, Wei & Yang, Simon X. & Wu, Haixia, 2009. "On robust stability of uncertain stochastic neural networks with distributed and interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2095-2104.
    5. Liu, Xiwei & Chen, Tianping, 2008. "Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2952-2962.
    6. Chendur Kumaran, R. & Venkatesh, T.G. & Swarup, K.S., 2022. "Stochastic delay differential equations: Analysis and simulation studies," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    7. Lin, Yi-Kuei, 2010. "Reliability evaluation of a revised stochastic flow network with uncertain minimum time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1253-1258.
    8. Feng, Wei & Yang, Simon X. & Fu, Wei & Wu, Haixia, 2009. "Robust stability analysis of uncertain stochastic neural networks with interval time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 414-424.
    9. Shu, Huisheng & Wang, Zidong & Lü, Zengwei, 2009. "Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 490-505.

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