General solution to a weakly delayed planar linear discrete system, the case of real different eigenvalues of the matrix of nondelayed terms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F22%3APU144283" target="_blank" >RIV/00216305:26110/22:PU144283 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/5.0081842" target="_blank" >https://doi.org/10.1063/5.0081842</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0081842" target="_blank" >10.1063/5.0081842</a>

Result language
angličtina
Original language name
General solution to a weakly delayed planar linear discrete system, the case of real different eigenvalues of the matrix of nondelayed terms
Original language description
The paper considers a linear discrete system with a single delay $$ x(k+1)=Ax(k)+B(k)x(k-m) $$ where $kinmathbb{Z}_0^{infty}:={0,1,dots,infty}$, $xcolon {mathbb{Z}}_0^{infty}tomathbb{R}^2$, $m$ is a positive fixed integer, $A={a_{ij}}_{i,j=1}^2$ and the entries of matrix $B={b_{ij}(k)}_{i,j=1}^2$ are defined for every $kinmathbb{Z}_0^{infty}$. It is assumed that the system is weakly delayed and the eigenvalues of the matrix $A$ are real and different. Analyzing and simplifying a formula for the general solution derived recently, it is shown that, for $kge m$, the number of arbitrary constants in this solution can be reduced to two. %rather than to $2(m + 1)$. Conditional stability of a given system is considered. In addition, a~non-delayed planar linear discrete system is constructed such that, for $kge m$ and after a transformation, we get the same solutions as those of the delayed system.
Czech name
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Czech description
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Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020
ISBN
978-0-7354-4182-8
ISSN
0094-243X
e-ISSN
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Number of pages
4
Pages from-to
„270009-1“-„270009-4“
Publisher name
American Institute of Physics
Place of publication
Melville (USA)
Event location
Rhodes, Greece
Event date
Sep 17, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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