Publication detail

Non-delayed Linear Planar Discrete Systems with Constant Coefficients Equivalent to Linear Planar Discrete Delayed Systems with Constant Coefficients

DIBLÍK, J. HARTMANOVÁ, M.

Original Title

Non-delayed Linear Planar Discrete Systems with Constant Coefficients Equivalent to Linear Planar Discrete Delayed Systems with Constant Coefficients

Type

article in a collection out of WoS and Scopus

Language

English

Original Abstract

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.

Keywords

planar delayed system; weak delay; initial problem; equivalent discrete system; general solution

Authors

DIBLÍK, J.; HARTMANOVÁ, M.

Released

20. 6. 2024

Publisher

Univerzita Obrany

Location

Brno

ISBN

978-80-7582-493-6

Book

Matematika, informační technologie a aplikované vědy, MITAV 2024

Edition number

I

Pages from

1

Pages to

9

Pages count

9

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"
}