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Novel Lyapunov–Krasovskii functional with delay-dependent matrix for stability of time-varying delay systems

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  • Kwon, W.
  • Koo, Baeyoung
  • Lee, S.M.

Abstract

This paper investigates the stability criteria of time-varying delay systems with known bounds of the delay and its derivative. To obtain a tighter bound of integral term, quadratic generalized free-weighting matrix inequality (QGFMI) is proposed. Furthermore, a novel augmented Lyapunov–Krasovskii functional (LKF) are constructed with a delay-dependent matrix, which impose the information for a bound of delay derivative. Relaxed stability condition using QGFMI and LKF provides a larger delay bound with low computational burden. The superiority of the proposed stability condition is verified by comparing to recent results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:149-157
    DOI: 10.1016/j.amc.2017.09.036
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    References listed on IDEAS

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    1. Liu, Xin-Ge & Wu, Min & Martin, Ralph & Tang, Mei-Lan, 2007. "Delay-dependent stability analysis for uncertain neutral systems with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 15-27.
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    6. Tang, Ze & Park, Ju H. & Lee, Tae H., 2016. "Dynamic output-feedback-based H∞ design for networked control systems with multipath packet dropouts," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 121-133.
    7. Wang, Zhanshan & Ding, Sanbo & Zhang, Huaguang, 2017. "Hierarchy of stability criterion for time-delay systems based on multiple integral approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 422-428.
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    Cited by:

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    2. 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.
    3. 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.
    4. Wenyong Duan & Yan Li & Jian Chen & Lin Jiang, 2019. "New Results on Stability Analysis of Uncertain Neutral-Type Lur’e Systems Derived from a Modified Lyapunov-Krasovskii Functional," Complexity, Hindawi, vol. 2019, pages 1-20, April.
    5. Wang, Yingchun & Zhang, Jiaxin & Zhang, Huaguang & Xie, Xiangpeng, 2021. "Finite-time adaptive neural control for nonstrict-feedback stochastic nonlinear systems with input delay and output constraints," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    6. 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).
    7. Pan, X.Z. & Huang, J.J. & Lee, S.M., 2023. "A novel convex relaxation technique on affine transformed sampled-data control issue for fuzzy semi-Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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