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Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System

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Abstract

This paper gives the controllability and Ulam–Hyers–Rassias (U–H–R) stability results for non-instantaneous impulsive stochastic multiple delays system with nonpermutable variable coefficients. The solution for nonlinear non-instantaneous impulsive stochastic systems is presented without the assumption of commutative property on delayed matrix coefficients. The kernel function of the solution operator is defined by sum of noncommutative products of delayed matrix constant coefficients. Sufficient conditions for controllability of linear and nonlinear non-instantaneous impulsive stochastic multiple delays system are established by using the Mönch fixed-point theorem under the proof that the corresponding linear system is controllable. Thereafter, U–H–R stability result is proved. Finally, the theoretical results are verified by a numerical example.

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Acknowledgements

This work is supported by Fundamental Research Grant Scheme, Ministry of Higher Education, Malaysia under Grant No. FRGS/1/2020/STG06/UCSI/02/1 and UCSI University Grants, Malaysia under Grant No. REIG-IASDA-2023/045. Also, the Authors thank Editor and anonymous reviewers for their valuable comments and suggestions for improving the quality of the manuscript up to this level.

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Authors and Affiliations

  1. Institute of Actuarial Science and Data Analytics, UCSI University, 56000, Kuala Lumpur, Malaysia

    T. Sathiyaraj

  2. Division of Mathematics, Saveetha School of Engineering, Saveetha University, Chennai, TamilNadu, 602 105, India

    T. Sathiyaraj

  3. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    JinRong Wang

  4. Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company, Guizhou University, Guiyang, 550025, Guizhou, China

    JinRong Wang

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Correspondence to T. Sathiyaraj.

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Communicated by Stefan Ulbrich.

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Sathiyaraj, T., Wang, J. Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02430-5

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