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Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities

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  • Du, Feifei
  • Lu, Jun-Guo

Abstract

This paper is concerned with finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities. By use of the method of steps and the generalized Gronwall inequality, a new criterion on finite-time stability is obtained. Two numerical examples are given to illustrate the effectiveness of our main results.

Suggested Citation

  • Du, Feifei & Lu, Jun-Guo, 2020. "Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300485
    DOI: 10.1016/j.amc.2020.125079
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    References listed on IDEAS

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    1. Pang Denghao & Jiang Wei, 2014. "Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-4, February.
    2. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    3. Hai Zhang & Renyu Ye & Song Liu & Jinde Cao & Ahmad Alsaedi & Xiaodi Li, 2018. "LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 537-545, February.
    4. Feifei Wang & Diyi Chen & Xinguang Zhang & Yonghong Wu, 2017. "Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(5), pages 984-993, April.
    5. Zhou, Xian-Feng & Yang, Fuli & Jiang, Wei, 2015. "Analytic study on linear neutral fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 295-307.
    6. Čermák, Jan & Došlá, Zuzana & Kisela, Tomáš, 2017. "Fractional differential equations with a constant delay: Stability and asymptotics of solutions," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 336-350.
    7. Wang, Ying & Liu, Lishan & Zhang, Xinguang & Wu, Yonghong, 2015. "Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 312-324.
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    Cited by:

    1. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Zhang, Shaohua & Wang, Cong & Zhang, Hongli & Ma, Ping & Li, Xinkai, 2022. "Dynamic analysis and bursting oscillation control of fractional-order permanent magnet synchronous motor system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    5. Chen, Yuting & Li, Xiaoyan & Liu, Song, 2021. "Finite-time stability of ABC type fractional delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    8. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    9. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    10. Zhao, Liuwei & Jin, Shuai & Jiang, Hongyun, 2022. "Investigation of complex dynamics and chaos control of the duopoly supply chain under the mixed carbon policy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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