IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v314y2017icp422-428.html
   My bibliography  Save this article

Hierarchy of stability criterion for time-delay systems based on multiple integral approach

Author

Listed:
  • Wang, Zhanshan
  • Ding, Sanbo
  • Zhang, Huaguang

Abstract

Taking a class of time-delay systems as research object, this brief aims at developing a theoretical support on the hierarchy of stability criterion which is derived by the multiple integral approach and free-weighting matrix technique. The hierarchy implies that the conservatism of stability criterion can be reduced by increasing the ply of integral terms in Lyapunov–Krasovskii functional (LKF). Together with three numerical experiments, the hierarchy of stability criterion is further shown.

Suggested Citation

  • Wang, Zhanshan & Ding, Sanbo & Zhang, Huaguang, 2017. "Hierarchy of stability criterion for time-delay systems based on multiple integral approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 422-428.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:422-428
    DOI: 10.1016/j.amc.2017.07.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317304678
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.07.016?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. Gyurkovics, É. & Szabó-Varga, G. & Kiss, K., 2017. "Stability analysis of linear systems with interval time-varying delays utilizing multiple integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 164-177.
    2. 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.
    3. Hien, Le Van & Trinh, Hieu, 2016. "Exponential stability of time-delay systems via new weighted integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 335-344.
    4. Li, Ruoxia & Cao, Jinde, 2016. "Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term," Applied Mathematics and Computation, Elsevier, vol. 278(C), pages 54-69.
    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. Tian, Yufeng & Wang, Zhanshan, 2021. "A new result on H∞ performance state estimation for static neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    2. Long, Fei & Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Wang, Qing-Guo & Wu, Min, 2018. "Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 224-242.
    3. Long, Fei & Jiang, Lin & He, Yong & Wu, Min, 2019. "Stability analysis of systems with time-varying delay via novel augmented Lyapunov–Krasovskii functionals and an improved integral inequality," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 325-337.
    4. 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.

    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. 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.
    2. 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.
    3. 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).
    4. Gyurkovics, É. & Szabó-Varga, G. & Kiss, K., 2017. "Stability analysis of linear systems with interval time-varying delays utilizing multiple integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 164-177.
    5. 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).
    6. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    7. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    8. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    9. 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.
    10. Maharajan, C. & Raja, R. & Cao, Jinde & Rajchakit, G. & Tu, Zhengwen & Alsaedi, Ahmed, 2018. "LMI-based results on exponential stability of BAM-type neural networks with leakage and both time-varying delays: A non-fragile state estimation approach," Applied Mathematics and Computation, Elsevier, vol. 326(C), pages 33-55.
    11. Wang, Fen & Chen, Yuanlong, 2021. "Mean square exponential stability for stochastic memristor-based neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    12. Shuoting Wang & Kaibo Shi & Jin Yang, 2022. "Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional," Mathematics, MDPI, vol. 10(15), pages 1-14, August.
    13. Li, Lingchun & Shen, Mouquan & Zhang, Guangming & Yan, Shen, 2017. "H∞ control of Markov jump systems with time-varying delay and incomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 95-106.
    14. 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.
    15. Wang, Bo & Yan, Juan & Cheng, Jun & Zhong, Shouming, 2017. "New criteria of stability analysis for generalized neural networks subject to time-varying delayed signals," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 322-333.
    16. Chen, Wenbin & Lu, Junwei & Zhuang, Guangming & Gao, Fang & Zhang, Zhengqiang & Xu, Shengyuan, 2022. "Further results on stabilization for neutral singular Markovian jump systems with mixed interval time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    17. Li, Ruoxia & Gao, Xingbao & Cao, Jinde, 2019. "Non-fragile state estimation for delayed fractional-order memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 221-233.
    18. Dong, Zeyu & Wang, Xin & Zhang, Xian, 2020. "A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    19. Zhong, Qishui & Han, Sheng & Shi, Kaibo & Zhong, Shouming & Cai, Xiao & Kwon, Oh-Min, 2022. "Distributed secure sampled-data control for distributed generators and energy storage systems in microgrids under abnormal deception attacks," Applied Energy, Elsevier, vol. 326(C).
    20. Li, Ruoxia & Cao, Jinde & Alsaedi, Ahmad & Alsaadi, Fuad, 2017. "Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 37-51.

    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:314:y:2017:i:c:p:422-428. 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.