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Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties

Author

Listed:
  • Yujuan Tian

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Yuhan Yin

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Fei Wang

    (School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China)

  • Kening Wang

    (Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA)

Abstract

This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs into real and imaginary parts, some stability criteria in terms of complex-valued linear matrix inequalities (LMIs) are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed. Moreover, a new impulsive differential inequality is applied to resolve the difficulties caused by the mixed time delays and delayed impulse effects. Finally, an illustrative example is provided to back up our theoretical results.

Suggested Citation

  • Yujuan Tian & Yuhan Yin & Fei Wang & Kening Wang, 2022. "Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:526-:d:744116
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    References listed on IDEAS

    as
    1. Wei, Linna & Chen, Wu-Hua & Huang, Ganji, 2015. "Globally exponential stabilization of neural networks with mixed time delays via impulsive control," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 10-26.
    2. Liu, An & Huang, Xia & Fan, Yingjie & Wang, Zhen, 2021. "A control-interval-dependent functional for exponential stabilization of neural networks via intermittent sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    4. Wang, Zengyun & Liu, Xinzhi, 2019. "Exponential stability of impulsive complex-valued neural networks with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 143-157.
    5. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    6. Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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    Full references (including those not matched with items on IDEAS)

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