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Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay

Author

Listed:
  • Ahmed M. Elshenhab

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Xingtao Wang

    (School of Mathematics, Harbin Institute of Technology, Harbin 150001, China)

  • Omar Bazighifan

    (Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy)

  • Jan Awrejcewicz

    (Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland)

Abstract

Nonhomogeneous systems governed by second-order linear differential equations with pure delay are considered. As an application, the exact solutions of these systems and their delayed matrix functions are used to obtain the finite-time stability results. Our results extend and improve some previous results by removing some restrictive conditions. Finally, an example is provided to illustrate our theoretical results.

Suggested Citation

  • Ahmed M. Elshenhab & Xingtao Wang & Omar Bazighifan & Jan Awrejcewicz, 2022. "Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1359-:d:796912
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    References listed on IDEAS

    as
    1. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    2. Elshenhab, Ahmed M. & Wang, Xing Tao, 2021. "Representation of solutions of linear differential systems with pure delay and multiple delays with linear parts given by non-permutable matrices," Applied Mathematics and Computation, Elsevier, vol. 410(C).
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    Cited by:

    1. Selvam, Anjapuli Panneer & Govindaraj, Venkatesan, 2024. "Investigation of controllability and stability of fractional dynamical systems with delay in control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 89-104.
    2. Ghada AlNemer & Mohamed Hosny & Ramalingam Udhayakumar & Ahmed M. Elshenhab, 2024. "Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process," Mathematics, MDPI, vol. 12(11), pages 1-15, June.
    3. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.
    4. Barakah Almarri & Xingtao Wang & Ahmed M. Elshenhab, 2022. "Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    5. Ahmed M. Elshenhab & Xingtao Wang & Clemente Cesarano & Barakah Almarri & Osama Moaaz, 2022. "Finite-Time Stability Analysis of Fractional Delay Systems," Mathematics, MDPI, vol. 10(11), pages 1-11, May.

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