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Exponential input-to-state stability of quaternion-valued neural networks with time delay

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  • Qi, Xingnan
  • Bao, Haibo
  • Cao, Jinde

Abstract

This paper debated the exponential input-to-state stability (EITSS) of the solution for a kind of quaternion-valued neural networks (QVNNs) with time delay. It fills the blank of QVNN in the aspect of input-to-state stability (ITSS). In virtue of the quaternion multiplication is not suitable for commutative law, QVNN is ordinarily resolved into four real-valued neural networks (RVNNs). Making use of a novel Lyapunov–Krasovskii function and some inequalities, we obtain a little sufficient conditions to assure the considered system is EITSS. Finally, by means of two examples, it is certified that the calculation results in this paper are fine.

Suggested Citation

  • Qi, Xingnan & Bao, Haibo & Cao, Jinde, 2019. "Exponential input-to-state stability of quaternion-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 382-393.
    • Handle: RePEc:eee:apmaco:v:358:y:2019:i:c:p:382-393
    DOI: 10.1016/j.amc.2019.04.045
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    Cited by:

    1. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun & Cao, Jinde, 2020. "Global Mittag-Leffler synchronization of fractional-order delayed quaternion-valued neural networks: Direct quaternion approach," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. Chen, Yuan & Wu, Jianwei & Bao, Haibo, 2022. "Finite-time stabilization for delayed quaternion-valued coupled neural networks with saturated impulse," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    4. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.
    5. Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    6. Cui, Qian & Li, Lulu & Lu, Jianquan & Alofi, Abdulaziz, 2022. "Finite-time synchronization of complex dynamical networks under delayed impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    7. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    8. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
    9. Li, Hong-Li & Kao, Yonggui & Hu, Cheng & Jiang, Haijun & Jiang, Yao-Lin, 2021. "Robust exponential stability of fractional-order coupled quaternion-valued neural networks with parametric uncertainties and impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    10. Mo, Wenjun & Bao, Haibo, 2022. "Finite-time synchronization for fractional-order quaternion-valued coupled neural networks with saturated impulse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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