IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp672-688.html
   My bibliography  Save this article

Novel inequality with application to improve the stability criterion for dynamical systems with two additive time-varying delays

Author

Listed:
  • Xiong, Lianglin
  • Cheng, Jun
  • Cao, Jinde
  • Liu, Zixin

Abstract

In this paper, the stability of the system with two additive time-varying delay components is studied and improved stability condition is obtained. It firstly establishes two novel integral inequalities, which are better than the same type inequalities found in the literature. Secondly, a new constructed Lyapunov functional is constructed based on the additive time-varying delays property. Following two steps to handle the Lyapunov functional, the delay-dependent stability condition is obtained which in terms of linear matrix inequalities. Finally, two numerical examples are given to verify the effectiveness of the proposed method and the superiority of the results.

Suggested Citation

  • Xiong, Lianglin & Cheng, Jun & Cao, Jinde & Liu, Zixin, 2018. "Novel inequality with application to improve the stability criterion for dynamical systems with two additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 672-688.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:672-688
    DOI: 10.1016/j.amc.2017.11.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317308020
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.11.020?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. 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.
    2. Lee, Seok Young & Lee, Won Il & Park, PooGyeon, 2017. "Improved stability criteria for linear systems with interval time-varying delays: Generalized zero equalities approach," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 336-348.
    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. Zhang, Bao-Lin & Cheng, Luhua & Pan, Kejia & Zhang, Xian-Ming, 2020. "Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Wang, Bo & Cheng, Jun & Zhou, Xia, 2020. "A multiple hierarchical structure strategy to quantized control of Markovian switching systems," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. Bo Li & Xiaobing Zhou & Yun Wang, 2019. "Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems," Complexity, Hindawi, vol. 2019, pages 1-9, November.
    4. Liu, Duyu & Liu, Xinzhi & Chen, Hao & Zhong, Shouming, 2020. "A PAIM control scheme on hybrid system with its application on SIDO buck converter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    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. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.

    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. 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).
    2. 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).
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. Kwon, O.M. & Lee, S.H. & Park, M.J. & Lee, S.M., 2020. "Augmented zero equality approach to stability for linear systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    8. 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).
    9. Gao, Zhen-Man & He, Yong & Wu, Min, 2019. "Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov–Krasovskii functional," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 258-269.
    10. 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.
    11. Subramanian, K. & Muthukumar, P. & Lakshmanan, S., 2018. "State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 267-281.
    12. 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.
    13. Zhang, Zhi-Ming & He, Yong & Wu, Min & Wang, Qing-Guo, 2017. "Exponential synchronization of chaotic neural networks with time-varying delay via intermittent output feedback approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 121-132.
    14. Qian, Wei & Liu, Haibo & Zhao, Yunji & Li, Yalong, 2022. "Delay-probability-dependent state estimation for neural networks with hybrid delays," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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).
    20. 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).

    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:321:y:2018:i:c:p:672-688. 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.