IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v404y2021ics009630032100312x.html
   My bibliography  Save this article

Hierarchical stability conditions of systems with time-varying delay

Author

Listed:
  • Zeng, Hong-Bing
  • Zhai, Zheng-Liang
  • Wang, Wei

Abstract

This paper studies the stability problem of time-varying delay systems. Firstly, By constructing a delay-product Lyapunov-Krasovskii functional, a stability criterion is established, where the advantages of convexity properties are being exploited. This stability criterion in terms of linear matrix inequality (LMI) can be checked exactly using an improved negativity condition of quadratic polynomials. It is demonstrated in the numeric examples that the proposed method can greatly reduce the conservativeness without leading to increase the number of decision variables.

Suggested Citation

  • Zeng, Hong-Bing & Zhai, Zheng-Liang & Wang, Wei, 2021. "Hierarchical stability conditions of systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    • Handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s009630032100312x
    DOI: 10.1016/j.amc.2021.126222
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630032100312X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126222?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Dongji & Chen, Fei & Meng, Bo & Hu, Xingliu & Wang, Jing, 2021. "Event-based secure H∞ load frequency control for delayed power systems subject to deception attacks," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    2. Liu, Yu-An & Tang, Shengdao & Liu, Yufan & Kong, Qingkai & Wang, Jing, 2021. "Extended dissipative sliding mode control for nonlinear networked control systems via event-triggered mechanism with random uncertain measurement," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    3. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
    4. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Yibo & Hua, Changchun & Park, PooGyeon & Qian, Cheng, 2023. "Stability criteria for time-varying delay systems via an improved reciprocally convex inequality lemma," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    2. Zhang, He & Xu, Shengyuan & Zhang, Zhengqiang & Chu, Yuming, 2022. "Practical stability of a nonlinear system with delayed control input," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    3. Chang, Xu-Kang & He, Yong & Gao, Zhen-Man, 2023. "Exponential stability of neural networks with a time-varying delay via a cubic function negative-determination lemma," Applied Mathematics and Computation, Elsevier, vol. 438(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Jun & Park, Ju H., 2020. "New versions of Bessel–Legendre inequality and their applications to systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Wu, Jiacheng & Su, Lei & Li, Shaoming & Wang, Jing & Chen, Xiangyong, 2021. "Extended dissipative filtering for singularly perturbed systems with random uncertain measurement: A double-layer switching mechanism," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    3. Yang, Yi & Chen, Fei & Lang, Jiahong & Chen, Xiangyong & Wang, Jing, 2021. "Sliding mode control of persistent dwell-time switched systems with random data dropouts," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    4. de Oliveira, Fúlvia S.S. & Souza, Fernando O., 2020. "Further refinements in stability conditions for time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Arunagirinathan, S. & Lee, T.H., 2024. "Generalized delay-dependent reciprocally convex inequality on stability for neural networks with time-varying delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 109-120.
    6. Lee, S.H. & Park, M.J. & Kwon, O.M. & Choi, S.G., 2022. "Less conservative stability criteria for general neural networks through novel delay-dependent functional," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    7. Long, Changqing & Zhang, Guodong & Hu, Junhao, 2021. "Fixed-time synchronization for delayed inertial complex-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    8. Zhang, Juan & Zhang, Huaguang & Cai, Yuliang & Wang, Wei, 2021. "Consensus control for nonlinear multi-agent systems with event-triggered communications," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    9. Jung, H.I. & Han, S.Y. & Singh, Satnesh & Lee, S.M., 2021. "Polynomially parameter dependent exponential stabilization of sampled-data LPV systems," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    10. Jiang, Xiaowei & Chen, Xiangyong & Chi, Ming & Chen, Jie, 2020. "On Hopf bifurcation and control for a delay systems," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    11. Li, Xiaoqing & She, Kun & Zhong, Shouming & Shi, Kaibo & Kang, Wei & Cheng, Jun & Yu, Yongbin, 2018. "Extended robust global exponential stability for uncertain switched memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 271-290.
    12. Wu, Tianyu & Huang, Xia & Chen, Xiangyong & Wang, Jing, 2020. "Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    13. Wang, Jinling & Liang, Jinling & Zhang, Cheng-Tang & Fan, Dongmei, 2021. "Event-triggered non-fragile control for uncertain positive Roesser model with PDT switching mechanism," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    14. Xinghua Liu & Siwei Qiao & Zhiwei Liu, 2023. "A Survey on Load Frequency Control of Multi-Area Power Systems: Recent Challenges and Strategies," Energies, MDPI, vol. 16(5), pages 1-22, February.
    15. Ding, Hongfei & Wang, Yudong & Shen, Hao, 2024. "A reinforcement learning integral sliding mode control scheme against lumped disturbances in hot strip rolling," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    16. Kwon, W. & Koo, Baeyoung & Lee, S.M., 2018. "Novel Lyapunov–Krasovskii functional with delay-dependent matrix for stability of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 149-157.
    17. Yupeng Shi & Dayong Ye, 2023. "Stability Analysis of Delayed Neural Networks via Composite-Matrix-Based Integral Inequality," Mathematics, MDPI, vol. 11(11), pages 1-13, May.
    18. Liu, Xiaonan & Kao, Yonggui, 2021. "Aperiodically intermittent pinning outer synchronization control for delayed complex dynamical networks with reaction-diffusion terms," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    19. Wang, Dongji & Chen, Fei & Meng, Bo & Hu, Xingliu & Wang, Jing, 2021. "Event-based secure H∞ load frequency control for delayed power systems subject to deception attacks," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    20. Ding, Chen & Ma, Li & Ding, Shihong, 2021. "Second-order sliding mode controller design with mismatched term and time-varying output constraint," Applied Mathematics and Computation, Elsevier, vol. 407(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:404:y:2021:i:c:s009630032100312x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.