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

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  • 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.

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
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    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).

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