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A formula for the lower Bohl exponent of discrete time-varying systems

Adam Czornik Krzysztof Simek
Archives of Control Sciences | 2023 | vol. 33 | No 2 | 413-424 | DOI: 10.24425/acs.2023.146282
Keywords time-varying systems asymptotic stability Bohl exponent
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Abstract

In this note, a formula for the lower Bohl exponent of a discrete system with variable coefficients and weak variation was proved. This formula expresses the Bohl exponent through the eigenvalues of the coefficient matrix. Based on these formulas a necessary and sufficient condition for an uniform exponential instability of such systems is also presented.
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Authors and Affiliations

Adam Czornik
1
Krzysztof Simek
1
  1. Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science, Akademicka Street 16, 44-101 Gliwice, Poland

Sufficient conditions for uniform global asymptotic stabilization of affine discrete-time systems with periodic coefficients

Adam Czornik Evgenii Makarov Michał Niezabitowski Svetlana Popova Vasilii Zaitsev
Archives of Control Sciences | 2021 | vol. 31 | No 1 | 81-98 | DOI: 10.24425/acs.2021.136881
Keywords discrete-time systems periodic systems affine systems uniform global asymptotic stabilization state feedback
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Abstract

Affine discrete-time control periodic systems are considered. The problem of global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has the Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Examples of using the obtained results are presented.
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Authors and Affiliations

Adam Czornik
1
Evgenii Makarov
2
Michał Niezabitowski
3
Svetlana Popova
4
Vasilii Zaitsev
4
  1. Faculty of Automatic Control, Electronics and Computer Science, Silesian University of Technology, 44-100 Gliwice, Poland
  2. Institute of Mathematics, National Academy of Sciencesof Belarus, 220072 Minsk, Belarus
  3. Faculty of Automatic Control, Electronics and Computer Science,Silesian University of Technology, 44-100 Gliwice, Poland
  4. Udmurt State University, 426034 Izhevsk, Russia

On a continuity of characteristic exponents of linear discrete time-varying systems

Adam Czornik Michał Niezabitowski Piotr Mokry
Archives of Control Sciences | 2012 | No 1 | DOI: 10.2478/v10170-011-0009-z
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Authors and Affiliations

Adam Czornik
Michał Niezabitowski
ORCID: ORCID
Piotr Mokry

Variation of constant formulas for fractional difference equations

Pham The Anh Artur Babiarz Adam Czornik Michał Niezabitowski Stefan Siegmund
Archives of Control Sciences | 2018 | vol. 28 | No 4 | 617–633 | DOI: 10.24425/acs.2018.125486
Keywords fractional difference equation variation of constant separation of solutions
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Abstract

In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.

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Authors and Affiliations

Pham The Anh
Artur Babiarz
Adam Czornik
Michał Niezabitowski
ORCID: ORCID
Stefan Siegmund

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