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Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

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.

Suggested Citation

  • Barakah Almarri & Xingtao Wang & Ahmed M. Elshenhab, 2022. "Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4223-:d:970535
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    References listed on IDEAS

    as
    1. Hamdy M. Ahmed, 2015. "Semilinear Neutral Fractional Stochastic Integro-Differential Equations with Nonlocal Conditions," Journal of Theoretical Probability, Springer, vol. 28(2), pages 667-680, June.
    2. Maejima, Makoto & Tudor, Ciprian A., 2013. "On the distribution of the Rosenblatt process," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1490-1495.
    3. Elshenhab, Ahmed M. & Wang, Xing Tao, 2021. "Representation of solutions of linear differential systems with pure delay and multiple delays with linear parts given by non-permutable matrices," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    4. Ahmed M. Elshenhab & Xingtao Wang & Clemente Cesarano & Barakah Almarri & Osama Moaaz, 2022. "Finite-Time Stability Analysis of Fractional Delay Systems," Mathematics, MDPI, vol. 10(11), pages 1-11, May.
    5. Ahmed M. Elshenhab & Xingtao Wang & Omar Bazighifan & Jan Awrejcewicz, 2022. "Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay," Mathematics, MDPI, vol. 10(9), pages 1-10, April.
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