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Relative Controllability and Ulam–Hyers Stability of the Second-Order Linear Time-Delay Systems

Author

Listed:
  • Kinda Abuasbeh

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia)

  • Nazim I. Mahmudov

    (Department of Mathematics, Eastern Mediterranean University, T.R. Northen Cyprus, Famagusta 99628, Turkey)

  • Muath Awadalla

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf 31982, Al Ahsa, Saudi Arabia)

Abstract

We introduce the delayed sine/cosine-type matrix function and use the Laplace transform method to obtain a closed form solution to IVP for a second-order time-delayed linear system with noncommutative matrices A and Ω . We also introduce a delay Gramian matrix and examine a relative controllability linear/semi-linear time delay system. We have obtained the necessary and sufficient condition for the relative controllability of the linear time-delayed second-order system. In addition, we have obtained sufficient conditions for the relative controllability of the semi-linear second-order time-delay system. Finally, we investigate the Ulam–Hyers stability of a second-order semi-linear time-delayed system.

Suggested Citation

  • Kinda Abuasbeh & Nazim I. Mahmudov & Muath Awadalla, 2023. "Relative Controllability and Ulam–Hyers Stability of the Second-Order Linear Time-Delay Systems," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:806-:d:1058343
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    Cited by:

    1. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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