Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Artur Babiarz; Irina Banshchikova; Adam Czornik; Evgeniĭ Makarov; Michał Niezabitowski; Svetlana Popova

doi:10.1007/978-3-030-35502-9_5

Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Artur Babiarz
, Irina Banshchikova
, Adam Czornik
, Evgeniĭ Makarov
, Michał Niezabitowski
, Svetlana Popova

Department of Automatic Control and Robotics (RAU/RAU3)

Udmurt State University
Belarus Academy of Sciences
University of Silesia in Katowice

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

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 [2–4] 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.

Original language	English
Title of host publication	Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018
Editors	Martin Bohner, Stefan Siegmund, Roman Šimon Hilscher, Petr Stehlík
Publisher	Springer
Pages	133-147
Number of pages	15
ISBN (Print)	9783030355012
DOIs	https://doi.org/10.1007/978-3-030-35502-9_5
Publication status	Published - 2020
Event	24th International Conference on Difference Equations and Applications, ICDEA 2018 - Dresden, Germany Duration: 21 May 2018 → 25 May 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	312
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	24th International Conference on Difference Equations and Applications, ICDEA 2018
Country/Territory	Germany
City	Dresden
Period	21/05/18 → 25/05/18

Keywords

Controllability
Discrete linear time-varying system
Lyapunov spectrum
Pole placement problem

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-030-35502-9_5

Cite this

Babiarz, A., Banshchikova, I., Czornik, A., Makarov, E., Niezabitowski, M., & Popova, S. (2020). Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems. In M. Bohner, S. Siegmund, R. Šimon Hilscher, & P. Stehlík (Eds.), Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018 (pp. 133-147). (Springer Proceedings in Mathematics and Statistics; Vol. 312). Springer. https://doi.org/10.1007/978-3-030-35502-9_5

Babiarz, Artur ; Banshchikova, Irina ; Czornik, Adam et al. / Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems. Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018. editor / Martin Bohner ; Stefan Siegmund ; Roman Šimon Hilscher ; Petr Stehlík. Springer, 2020. pp. 133-147 (Springer Proceedings in Mathematics and Statistics).

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title = "Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems",

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{\textendash}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.",

keywords = "Controllability, Discrete linear time-varying system, Lyapunov spectrum, Pole placement problem",

author = "Artur Babiarz and Irina Banshchikova and Adam Czornik and Evgeniĭ Makarov and Micha{\l} Niezabitowski and Svetlana Popova",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 24th International Conference on Difference Equations and Applications, ICDEA 2018 ; Conference date: 21-05-2018 Through 25-05-2018",

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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 M Bohner, S Siegmund, R Šimon Hilscher & P Stehlík (eds), Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018. Springer Proceedings in Mathematics and Statistics, vol. 312, Springer, pp. 133-147, 24th International Conference on Difference Equations and Applications, ICDEA 2018, Dresden, Germany, 21/05/18. https://doi.org/10.1007/978-3-030-35502-9_5

Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems. / Babiarz, Artur; Banshchikova, Irina; Czornik, Adam et al.
Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018. ed. / Martin Bohner; Stefan Siegmund; Roman Šimon Hilscher; Petr Stehlík. Springer, 2020. p. 133-147 (Springer Proceedings in Mathematics and Statistics; Vol. 312).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

AU - Babiarz, Artur

AU - Banshchikova, Irina

AU - Czornik, Adam

AU - Makarov, Evgeniĭ

AU - Niezabitowski, Michał

AU - Popova, Svetlana

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - 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 [2–4] 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.

AB - 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 [2–4] 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.

KW - Controllability

KW - Discrete linear time-varying system

KW - Lyapunov spectrum

KW - Pole placement problem

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AN - SCOPUS:85080858350

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BT - Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018

A2 - Bohner, Martin

A2 - Siegmund, Stefan

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Babiarz A, Banshchikova I, Czornik A, Makarov E, Niezabitowski M, Popova S. Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems. In Bohner M, Siegmund S, Šimon Hilscher R, Stehlík P, editors, Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018. Springer. 2020. p. 133-147. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-35502-9_5

Assignability of Lyapunov Spectrum for Discrete Linear Time-Varying Systems

Abstract

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Keywords

ASJC Scopus subject areas

Access to Document

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