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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020

ISBN

978-0-7354-4182-8

ISSN

0094-243X

e-ISSN

—

Počet stran výsledku

4

Strana od-do

„270009-1“-„270009-4“

Název nakladatele

American Institute of Physics

Místo vydání

Melville (USA)

Místo konání akce

Rhodes, Greece

Datum konání akce

17. 9. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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