IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v138y2020ics096007792030326x.html
   My bibliography  Save this article

Null controllability results for stochastic delay systems with delayed perturbation of matrices

Author

Listed:
  • Sathiyaraj, T.
  • Fečkan, Michal
  • Wang, JinRong

Abstract

In this paper, we adopt a notation of delayed perturbation of matrices to study controllability of stochastic delay systems in finite dimensional spaces. By using the delayed perturbation of matrix, we write an explicit formula of solutions to linear stochastic delay systems. We present the necessary and sufficient conditions for null controllability of linear stochastic delay systems by using perturbed controllability matrix and rank correlation method. Thereafter, sufficient conditions are derived for null controllability of semilinear stochastic delay systems under the proved results of corresponding linear stochastic system is null controllable, stochastic linear controllability operator, appropriate hypothesis on semilinear term and stochastic delay analysis techniques. The obtained theoretical results is verified through numerical simulation.

Suggested Citation

  • Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s096007792030326x
    DOI: 10.1016/j.chaos.2020.109927
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792030326X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109927?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mourad Kerboua & Amar Debbouche & Dumitru Baleanu, 2013. "Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    2. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    3. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    4. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    5. Amar Debbouche & Dumitru Baleanu, 2012. "Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-17, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vadivoo, B.S. & Jothilakshmi, G. & Almalki, Y. & Debbouche, A. & Lavanya, M., 2022. "Relative controllability analysis of fractional order differential equations with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    2. Kui Liu & Michal Fečkan & D. O’Regan & JinRong Wang, 2019. "Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    3. Criens, David & Niemann, Lars, 2024. "A class of multidimensional nonlinear diffusions with the Feller property," Statistics & Probability Letters, Elsevier, vol. 208(C).
    4. Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
    5. Vadivoo, B.Sundara & Raja, R. & Seadawy, R. Aly & Rajchakit, G., 2019. "Nonlinear integro-differential equations with small unknown parameters: A controllability analysis problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 15-26.
    6. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    7. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    8. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    9. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    10. Zhengqi Ma & Hongyin Jiang & Chun Li & Defei Zhang & Xiaoyou Liu, 2024. "Stochastic Intermittent Control with Uncertainty," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    11. Nutz, Marcel, 2015. "Robust superhedging with jumps and diffusion," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4543-4555.
    12. Denk, Robert & Kupper, Michael & Nendel, Max, 2020. "A semigroup approach to nonlinear Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1616-1642.
    13. Lin, Qian, 2019. "Jensen inequality for superlinear expectations," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 79-83.
    14. Yan Dolinsky & Halil Soner, 2013. "Duality and convergence for binomial markets with friction," Finance and Stochastics, Springer, vol. 17(3), pages 447-475, July.
    15. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    16. Lu, Liang & Liu, Zhenhai & Bin, Maojun, 2016. "Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 201-212.
    17. Moreau, Ludovic, 2012. "A contribution in stochastic control applied to finance and insurance," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/10711 edited by Bouchard, Bruno.
    18. Cai, Yi & Tang, Zhenpeng & Chen, Kaijie & Liu, Dinggao, 2023. "Quantifying the international stock market risk spillover: An analysis based on G-expectation upper variances," Finance Research Letters, Elsevier, vol. 58(PA).
    19. Nendel, Max, 2019. "On Nonlinear Expectations and Markov Chains under Model Uncertainty," Center for Mathematical Economics Working Papers 628, Center for Mathematical Economics, Bielefeld University.
    20. Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," The Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s096007792030326x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.