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

Author

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  • 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
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    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. 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.
    3. 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).
    4. 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.
    5. 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.
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    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).

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