TY - GEN
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
UR - https://www.scopus.com/pages/publications/85080858350
U2 - 10.1007/978-3-030-35502-9_5
DO - 10.1007/978-3-030-35502-9_5
M3 - Conference contribution
AN - SCOPUS:85080858350
SN - 9783030355012
T3 - Springer Proceedings in Mathematics and Statistics
SP - 133
EP - 147
BT - Difference Equations and Discrete Dynamical Systems with Applications - 24th ICDEA 2018
A2 - Bohner, Martin
A2 - Siegmund, Stefan
A2 - Šimon Hilscher, Roman
A2 - Stehlík, Petr
PB - Springer
T2 - 24th International Conference on Difference Equations and Applications, ICDEA 2018
Y2 - 21 May 2018 through 25 May 2018
ER -