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Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses

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Abstract

The objective of this paper is to establish the sufficient condition for the controllability of a control problem represented by second-order nonlinear differential equation with non-instantaneous impulses in a Hilbert space X. The results are obtained using the strongly continuous cosine family of linear operators and Banach fixed point method. Also, we study the controllability of the nonlocal as well as integro-differential systems. Finally, a few examples are provided to illustrate the applications of the obtained abstract results.

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Acknowledgements

We highly appreciate the valuable suggestions and comments from the anonymous referees and editor which helped us to improve the quality of the manuscript.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Kamand, (H.P.), 175 005, India

    Avadhesh Kumar & M. Muslim

  2. Department of Mathematics, Bharathiar University, Coimbatore, 641046, Tamilnadu, India

    R. Sakthivel

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea

    R. Sakthivel

Authors
  1. Avadhesh Kumar
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  2. M. Muslim
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  3. R. Sakthivel
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Correspondence to Avadhesh Kumar.

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Kumar, A., Muslim, M. & Sakthivel, R. Controllability of the Second-Order Nonlinear Differential Equations with Non-instantaneous Impulses. J Dyn Control Syst 24, 325–342 (2018). https://doi.org/10.1007/s10883-017-9376-5

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  • DOI: https://doi.org/10.1007/s10883-017-9376-5

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