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DIBLÍK, J. HARTMANOVÁ, M.
Originální název
Non-delayed Linear Planar Discrete Systems with Constant Coefficients Equivalent to Linear Planar Discrete Delayed Systems with Constant Coefficients
Typ
článek ve sborníku mimo WoS a Scopus
Jazyk
angličtina
Originální abstrakt
Planar linear discrete delayed systems w(k +1) = Aw(k)+Bw(k −m), k = 0,1,... are considered, where A and B are constant matrices and m is a positive integer denoting a delay. Recently, formulas have been derived for the general solution of such systems provided that one eigenvalue of A is nonzero while the other being zero, and that matrices A and B satisfy the conditions known for so-called weakly delayed systems. Conditions characterizing weakly delayed systems imply that there are only two roots of the relevant quasi-characteristic equation. The present paper is concerned with the problem of a possible replacement of the delayed systems in question with non-delayed planar ones x(k +1) = Cx(k), k = 0,1,... having an identical general solution. It is shown that this is possible if a transient interval is passed and possible forms of the matrix C are found. Some relationships with previously known results are commented.
Klíčová slova
planar delayed system; weak delay; initial problem; equivalent discrete system; general solution
Autoři
DIBLÍK, J.; HARTMANOVÁ, M.
Vydáno
20. 6. 2024
Nakladatel
Univerzita Obrany
Místo
Brno
ISBN
978-80-7582-493-6
Kniha
Matematika, informační technologie a aplikované vědy, MITAV 2024
Číslo edice
I
Strany od
1
Strany do
9
Strany počet
URL
https://mitav.unob.cz/data/final%20Program%20MITAV%202024.pdf
BibTex
@inproceedings{BUT188978, author="Josef {Diblík} and Marie {Hartmanová}", title="Non-delayed Linear Planar Discrete Systems with Constant Coefficients Equivalent to Linear Planar Discrete Delayed Systems with Constant Coefficients", booktitle="Matematika, informační technologie a aplikované vědy, MITAV 2024", year="2024", number="I", pages="1--9", publisher="Univerzita Obrany", address="Brno", isbn="978-80-7582-493-6", url="https://mitav.unob.cz/data/final%20Program%20MITAV%202024.pdf" }