Detail publikačního výsledku

Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis

DIBLÍK, J.; HALFAROVÁ, H.; ŠAFAŘÍK, J.

Originální název

Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis

Anglický název

Formulas for the general solution of weakly delayed planar linear discrete systems with constant coefficients and their analysis

Druh

Článek WoS

Originální abstrakt

The paper is concerned with weakly delayed linear discrete homogeneous planar systems with constant coefficients. By the method of Z-transform, formulas for the general solutions, dependent on the Jordan forms of the matrix of non-delayed linear terms, are derived and the influence is analyzed of the delay on the form of the general solutions. It is shown that, after several steps, the general solutions depend only on two arbitrary parameters which are linear combinations of the initial values. This property is used to prove results on conditional stability. Linear discrete homogeneous planar systems without delay are found to have the same general solutions as the initial one. The results are illustrated by examples. Previous results are analyzed, commented and improved.

Anglický abstrakt

The paper is concerned with weakly delayed linear discrete homogeneous planar systems with constant coefficients. By the method of Z-transform, formulas for the general solutions, dependent on the Jordan forms of the matrix of non-delayed linear terms, are derived and the influence is analyzed of the delay on the form of the general solutions. It is shown that, after several steps, the general solutions depend only on two arbitrary parameters which are linear combinations of the initial values. This property is used to prove results on conditional stability. Linear discrete homogeneous planar systems without delay are found to have the same general solutions as the initial one. The results are illustrated by examples. Previous results are analyzed, commented and improved.

Klíčová slova

Linear discrete system; Weakly delayed system; Jordan form; Planar system; Conditional stability

Klíčová slova v angličtině

Linear discrete system; Weakly delayed system; Jordan form; Planar system; Conditional stability

Autoři

DIBLÍK, J.; HALFAROVÁ, H.; ŠAFAŘÍK, J.

Rok RIV

2020

Vydáno

01.10.2019

Nakladatel

Elsevier

ISSN

0096-3003

Periodikum

APPLIED MATHEMATICS AND COMPUTATION

Svazek

358

Číslo

10

Stát

Spojené státy americké

Strany od

363

Strany do

381

Strany počet

18

URL

https://www.sciencedirect.com/science/article/pii/S0096300319302760?via%3Dihub

BibTex

@article{BUT157258,
  author="Josef {Diblík} and Hana {Boháčková} and Jan {Šafařík}",
  title="Formulas   for   the   general   solution   of   weakly   delayed   planar  linear   discrete   systems   with   constant   coefficients   and   their  analysis",
  journal="APPLIED MATHEMATICS AND COMPUTATION",
  year="2019",
  volume="358",
  number="10",
  pages="363--381",
  doi="10.1016/j.amc.2019.03.068",
  issn="0096-3003",
  url="https://www.sciencedirect.com/science/article/pii/S0096300319302760?via%3Dihub"
}