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Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovskiĭ Approach

Author

Listed:
  • Cemil Tunç

    (Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Osman Tunç

    (Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Campus, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Yuanheng Wang

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    These authors contributed equally to this work.)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
    These authors contributed equally to this work.)

Abstract

In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and boundedness of solutions of a perturbed system. We construct two appropriate Lyapunov–Krasovskiĭ functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov–Krasovskiĭ method. For illustration, two examples are provided in particular cases. An advantage of the new LKFs used here is that they allow to eliminate using Gronwall’s inequality. When we compare our results with recent results in the literature, the established conditions are more general, less restrictive and optimal for applications.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1196-:d:561813
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    References listed on IDEAS

    as
    1. Zerong Ren & Jun-kang Tian, 2020. "Stability Analysis of Systems with Interval Time-Varying Delays via a New Integral Inequality," Complexity, Hindawi, vol. 2020, pages 1-7, February.
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    Cited by:

    1. Khalid A. Alattas & Mai The Vu & Omid Mofid & Fayez F. M. El-Sousy & Abdullah K. Alanazi & Jan Awrejcewicz & Saleh Mobayen, 2022. "Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    2. 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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