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

Abuasbeh K., Mahmudov N., Awadalla M.

Mathematics, vol.11, no.4, 2023 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 11 Say: 4
  • Nəşr tarixi: 2023
  • Doi nömrəsi: 10.3390/math11040806
  • jurnalın adı: Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Açar sözlər: controllability, delay systems, fractional calculus, stability
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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 (Formula presented.). 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.