Relative Controllability and Ulam–Hyers Stability of the Second-Order Linear Time-Delay Systems-Reference-Cited by-同舟云学术

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

Published:2023-02-05 Issue:4 Volume:11 Page:806
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Abuasbeh Kinda¹^ORCID,Mahmudov Nazim I.²^ORCID,Awadalla Muath¹^ORCID

Affiliation:

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

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

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.

Funder

Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/4/806/pdf

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