Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process

Barakah Almarri, Xingtao Wang and Ahmed M. Elshenhab ()
Additional contact information
Barakah Almarri: Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Xingtao Wang: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Ahmed M. Elshenhab: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2022, vol. 10, issue 22, 1-20

Abstract: In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With the aid of the delayed matrix functions of these systems, we derive the controllability results as an application. By using a delay Gramian matrix, we provide sufficient and necessary criteria for the controllability of linear stochastic delay systems. In addition, by employing Krasnoselskii’s fixed point theorem, we present some necessary criteria for the controllability of nonlinear stochastic delay systems. Our results improve and extend some existing ones. Finally, an example is given to illustrate the main results.

Keywords: controllability; stochastic delay-differential equation; Rosenblatt process; delayed matrix function; delay Gramian matrix; Krasnoselskii’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/22/4223/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/22/4223/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:22:p:4223-:d:970535

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().