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Hierarchical stability conditions of systems with time-varying delay

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  • 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
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    References listed on IDEAS

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    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.
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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).
    2. 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).
    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).

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