Přístupnostní navigace
E-application
Search Search Close
Publication result detail
HALFAROVÁ, H.; DIBLÍK, J.; ŠAFAŘÍK, J.
Original Title
General solution to a weakly delayed planar linear discrete system, the case of real different eigenvalues of the matrix of nondelayed terms
English Title
Type
Paper in proceedings (conference paper)
Original Abstract
The paper considers a linear discrete system with a single delay $$ x(k+1)=Ax(k)+B(k)x(k-m) $$ where $k\in\mathbb{Z}_0^{\infty}:=\{0,1,\dots,\infty\}$, $x\colon {\mathbb{Z}}_0^{\infty}\to\mathbb{R}^2$, $m$ 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 $k\in\mathbb{Z}_0^{\infty}$. 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 $k\ge m$, 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 $k\ge m$ and after a transformation, we get the same solutions as those of the delayed system.
English abstract
Keywords
planar linear discrete system; constant coefficients; weakly delayed system
Key words in English
Authors
RIV year
2022
Released
06.04.2022
Publisher
American Institute of Physics
Location
Melville (USA)
ISBN
978-0-7354-4182-8
Book
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020
0094-243X
Periodical
AIP conference proceedings
Volume
2245
Number
1
State
United States of America
Pages from
270009-1
Pages to
270009-4
Pages count
4
URL
https://doi.org/10.1063/5.0081842