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

Kinda Abuasbeh (), Nazim I. Mahmudov () and Muath Awadalla
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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

Mathematics, 2023, vol. 11, issue 4, 1-19

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.

Keywords: stability; controllability; delay systems; fractional calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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