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New versions of Bessel–Legendre inequality and their applications to systems with time-varying delay

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  • Chen, Jun
  • Park, Ju H.

Abstract

This paper is concerned with the stability of linear time-delay systems by applying the Lyapunov–Krasovskii (L–K) functional method. Two versions of Bessel–Legendre (B-L) inequality are developed that are more suitable to deal with the stability problem of systems with a time-varying delay. Meanwhile, in order to take full advantage of the interest of the new versions of B-L inequality, a novel L–K functional is properly tailored by integrating the integral information of the state into quadratic and integral terms. As a result, more relaxed stability conditions are obtained, whose effectiveness is illustrated by two commonly-used numerical examples.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300291
    DOI: 10.1016/j.amc.2020.125060
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    References listed on IDEAS

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    1. Gyurkovics, É. & Szabó-Varga, G. & Kiss, K., 2017. "Stability analysis of linear systems with interval time-varying delays utilizing multiple integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 164-177.
    2. 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.
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    4. 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.
    5. 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.
    6. Gao, Zhen-Man & He, Yong & Wu, Min, 2019. "Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov–Krasovskii functional," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 258-269.
    7. 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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