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Exponential stability of uncertain stochastic neural networks with mixed time-delays

Author

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  • Wang, Zidong
  • Lauria, Stanislao
  • Fang, Jian’an
  • Liu, Xiaohui

Abstract

This paper is concerned with the global exponential stability analysis problem for a class of stochastic neural networks with mixed time-delays and parameter uncertainties. The mixed delays comprise discrete and distributed time-delays, the parameter uncertainties are norm-bounded, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. The purpose of the stability analysis problem is to derive easy-to-test criteria under which the delayed stochastic neural network is globally, robustly, exponentially stable in the mean square for all admissible parameter uncertainties. By resorting to the Lyapunov–Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established by using an efficient linear matrix inequality (LMI) approach. The proposed criteria can be checked readily by using recently developed numerical packages, where no tuning of parameters is required. An example is provided to demonstrate the usefulness of the proposed criteria.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:1:p:62-72
    DOI: 10.1016/j.chaos.2005.10.061
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    References listed on IDEAS

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    1. 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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    3. Hu, Jin & Zhong, Shouming & Liang, Li, 2006. "Exponential stability analysis of stochastic delayed cellular neural network," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1006-1010.
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    1. 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.
    2. Singh, Vimal, 2009. "Remarks on estimating upper limit of norm of delayed connection weight matrix in the study of global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2013-2017.
    3. 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.
    4. Liu, Duyu & Zhong, Shouming & Xiong, Lianglin, 2009. "On robust stability of uncertain neutral systems with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2332-2339.
    5. Zhang, Jinhui & Shi, Peng & Qiu, Jiqing, 2008. "Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 160-167.
    6. Singh, Vimal, 2009. "Novel global robust stability criterion for neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 348-353.
    7. Lu, Jun-Xiang & Ma, Yichen, 2008. "Mean square exponential stability and periodic solutions of stochastic delay cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1323-1331.
    8. Zhifu Jia & Cunlin Li, 2023. "Almost Sure Exponential Stability of Uncertain Stochastic Hopfield Neural Networks Based on Subadditive Measures," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    9. 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.
    10. 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.
    11. Gao, Ming & Cui, Baotong, 2009. "Global robust stability of neural networks with multiple discrete delays and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1823-1834.
    12. 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.
    13. Huang, Zaitang & Yang, Qi-Gui, 2009. "Existence and exponential stability of almost periodic solution for stochastic cellular neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 773-780.
    14. 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.
    15. 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.
    16. 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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