IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i17p3096-d900473.html
   My bibliography  Save this article

Stability Analysis for Time-Delay Systems via a New Negativity Condition on Quadratic Functions

Author

Listed:
  • Shenping Xiao

    (School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
    Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province, Zhuzhou 412007, China)

  • Jin Yu

    (School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China
    Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province, Zhuzhou 412007, China)

  • Simon X. Yang

    (Advanced Robotics and Intelligent Systems Laboratory, School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada)

  • Yongfeng Qiu

    (Guiyang Aluminum Magnesium Design and Research Institute Co., Ltd., Guiyang 550081, China
    School of Automation, Central South University, Changsha 410083, China)

Abstract

This article studies the stability problem of linear systems with time-varying delays. First, a new negative condition is established for a class of quadratic functions whose variable is within a closed set. Then, based on this new condition, a couple of stability criteria for the system under study are derived by constructing an appropriate Lyapunov–Krasovskii functional. Finally, it is demonstrated through two numerical examples that the proposed stability criteria are efficient and outperform some existing methods.

Suggested Citation

  • Shenping Xiao & Jin Yu & Simon X. Yang & Yongfeng Qiu, 2022. "Stability Analysis for Time-Delay Systems via a New Negativity Condition on Quadratic Functions," Mathematics, MDPI, vol. 10(17), pages 1-9, August.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3096-:d:900473
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/17/3096/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/17/3096/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cemil Tunç & Osman Tunç & Yuanheng Wang & Jen-Chih Yao, 2021. "Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovskiĭ Approach," Mathematics, MDPI, vol. 9(11), pages 1-20, May.
    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. Wenbin Chen & Fang Gao, 2019. "Stability analysis of systems via a new double free-matrix-based integral inequality with interval time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(14), pages 2663-2672, October.
    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.
    5. Chang-Hua Lien & Hao-Chin Chang & Ker-Wei Yu & Hung-Chi Li & Yi-You Hou, 2021. "Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    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. Wenqi Liao & Hongbing Zeng & Huichao Lin, 2024. "Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach," Mathematics, MDPI, vol. 12(11), pages 1-14, May.

    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. 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).
    2. 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).
    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. Chen, Wenbin & Gao, Fang & She, Jinhua & Xia, Weifeng, 2020. "Further results on delay-dependent stability for neutral singular systems via state decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    5. 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).
    6. Luo, Jinnan & Liu, Xinzhi & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Cheng, Jun, 2020. "A new approach to generalized dissipativity analysis for fuzzy systems with coupling memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    7. Zeng, Hong-Bing & Zhai, Zheng-Liang & He, Yong & Teo, Kok-Lay & Wang, Wei, 2020. "New insights on stability of sampled-data systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    8. Shen, Zhihao & Zhang, Liang & Niu, Ben & Zhao, Ning, 2023. "Event-based reachable set synthesis for delayed nonlinear semi-Markov systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    9. Abolpour, Roozbeh & Khayatian, Alireza & Dehghani, Maryam & Rokhsari, Alireza, 2023. "An Equivalent Condition for Stability Analysis of LTI Systems with Bounded Time-invariant Delay," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    10. 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).
    11. 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).
    12. Khalid A. Alattas & Mai The Vu & Omid Mofid & Fayez F. M. El-Sousy & Abdullah K. Alanazi & Jan Awrejcewicz & Saleh Mobayen, 2022. "Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    13. Dong-Hoon Lee & Yeong-Jae Kim & Seung-Hoon Lee & Oh-Min Kwon, 2024. "Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via an Augmented Lyapunov–Krasovskii Functional," Mathematics, MDPI, vol. 12(14), pages 1-19, July.
    14. Singh, Ajeet & Shukla, Anurag & Vijayakumar, V. & Udhayakumar, R., 2021. "Asymptotic stability of fractional order (1,2] stochastic delay differential equations in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    15. 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.
    16. Can Zhao & Kaibo Shi & Yiqian Tang & Shouming Zhong, 2022. "A New Slack Lyapunov Functional for Dynamical System with Time Delay," Mathematics, MDPI, vol. 10(23), pages 1-11, November.
    17. Huang, Yi-Bo & He, Yong, 2022. "Bessel-type inequality in semi-inner-product spaces and its application to stability analysis of discrete-time systems with distributed delays," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    18. Liang, Xingyue & Xia, Jianwei & Chen, Guoliang & Zhang, Huasheng & Wang, Zhen, 2019. "Dissipativity-based sampled-data control for fuzzy Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 552-564.
    19. 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).
    20. Han, Lihuan & Ma, Yuechao, 2024. "Learning-based asynchronous sliding mode control for semi-Markov jump systems with time-varying delay using relaxed negative-determination lemma," Chaos, Solitons & Fractals, Elsevier, vol. 179(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:gam:jmathe:v:10:y:2022:i:17:p:3096-:d:900473. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.