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Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

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Difference Equations and Discrete Dynamical Systems with Applications (ICDEA 2018)

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Abstract

We discuss relations between the four formulations of the problem of assignability of the Lyapunov spectrum for discrete linear time-varying systems by a time-varying feedback. For two of them: global assignability and proportional local assignability, we have already [2,3,4] obtained sufficient conditions in terms of uniform complete controllability and certain asymptotic properties of the free system. In the present paper we discuss the assumptions of our papers and demonstrate the use of the obtained conditions by numerical examples. We also compare our results with the classical pole placement problem. Finally, we formulate a couple of directions for further research in this area.

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Acknowledgements

The research presented here was done by the first and third author as part of the projects funded by the National Science Centre in Poland granted according to decisions DEC-2015/19/D/ST7/03679 and DEC-2017/25/B/ST7/02888, respectively. The research of M.N. was supported by the Polish National Agency for Academic Exchange according to the decision PPN/BEK/2018/1/00312/DEC/1. The research presented here by Banshchikova and Popova were supported by Russian Foundation for Basic Research (project no. 18–51–41005–Uzb).

Author information

Authors and Affiliations

  1. Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

    Artur Babiarz, Adam Czornik & Michał Niezabitowski

  2. Department of Differential Equations, Udmurt State University, Universitetskaya 1, Izhevsk, 426034, Russia

    Irina Banshchikova & Svetlana Popova

  3. National Academy of Sciences of Belarus, Institute of Mathematics, Surganova 11, Minsk, 220072, Belarus

    Evgeniĭ Makarov

  4. Faculty of Mathematics, Physics and Chemistry, University of Silesia, Institute of Mathematics, Bankowa 14, 40-007, Katowice, Poland

    Michał Niezabitowski

Authors
  1. Artur Babiarz
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  2. Irina Banshchikova
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  3. Adam Czornik
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  4. Evgeniĭ Makarov
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  5. Michał Niezabitowski
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  6. Svetlana Popova
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Corresponding author

Correspondence to Michał Niezabitowski .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

    Martin Bohner

  2. Institute for Analysis, CfD, Dresden University of Technology, Dresden, Germany

    Stefan Siegmund

  3. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

    Roman Šimon Hilscher

  4. Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    Petr Stehlík

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Babiarz, A., Banshchikova, I., Czornik, A., Makarov, E., Niezabitowski, M., Popova, S. (2020). Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems. In: Bohner, M., Siegmund, S., Šimon Hilscher, R., Stehlík, P. (eds) Difference Equations and Discrete Dynamical Systems with Applications. ICDEA 2018. Springer Proceedings in Mathematics & Statistics, vol 312. Springer, Cham. https://doi.org/10.1007/978-3-030-35502-9_5

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