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Relative Controllability of Impulsive Linear Discrete Delay Systems

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Abstract

This paper investigates relative controllability of impulsive linear discrete delay systems with constant coefficients and a pure delay. Grammian and rank criteria for relative controllability are respectively established by introducing an impulsive discrete delay Grammian matrix. Thereafter, the restricted relative controllability of impulsive linear discrete delay systems is studied. More precisely, when the terminal state locates in a special invariant linear subspace, Grammian and rank criteria for relative controllability are demonstrated and an expression of corresponding control function is constructed. Finally, an example is provided to illustrate theoretical results.

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Authors and Affiliations

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

    Xianghua Jin & JinRong Wang

  2. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, Fujian, China

    Xianghua Jin

  3. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, 842 48, Mlynská dolina, Bratislava, Slovakia

    Michal Fečkan

  4. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

  5. 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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  1. Xianghua Jin
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  2. Michal Fečkan
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  3. JinRong Wang
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All authors reviewed and agreed this revised manuscript.

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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (12161015), Guizhou Provincial Basic Research Program (Natural Science) [2023]034, and by the Slovak Grant Agency VEGA Nos. 1/0084/23 and 2/0127/20.

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Jin, X., Fečkan, M. & Wang, J. Relative Controllability of Impulsive Linear Discrete Delay Systems. Qual. Theory Dyn. Syst. 22, 133 (2023). https://doi.org/10.1007/s12346-023-00831-x

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