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Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach

Author

Listed:
  • Wenqi Liao

    (School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China)

  • Hongbing Zeng

    (School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou 412007, China)

  • Huichao Lin

    (College of Information Science and Engineering, Northeastern University, Shenyang 110819, China)

Abstract

This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints of traditional constant matrix-dependent zero equations. Secondly, for a class of periodic time-varying delays, considering the monotonicity of the delay and combining it with an augmented variable approach, Lyapunov functionals are constructed for monotonically increasing and monotonically decreasing delay intervals, respectively. Based on the constructed augmented Lyapunov functionals and the employed time-varying zero equation, less conservative stability criteria are obtained separately for bounded and periodic time-varying delays. Lastly, three examples are used to verify the superiority of the stability conditions obtained in this paper.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1638-:d:1400391
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    References listed on IDEAS

    as
    1. Liming Ding & Liqin Chen & Dajiang He & Weiwei Xiang, 2022. "New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems," Mathematics, MDPI, vol. 10(21), pages 1-13, November.
    2. Huichao Lin & Jiuxiang Dong, 2023. "Stability analysis of T–S fuzzy systems with time-varying delay via parameter-dependent reciprocally convex inequality," International Journal of Systems Science, Taylor & Francis Journals, vol. 54(6), pages 1289-1298, April.
    3. 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.
    4. 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.
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