Publication detail

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

DIBLÍK, J. HALFAROVÁ, H. ŠAFAŘÍK, J.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

01.10.2019

Publisher

Elsevier

ISBN

0096-3003

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Year of study

358

Number

10

State

US

Pages from

363

Pages to

381

Pages count

18

URL

Documents

BibTex


@article{BUT157258,
  author="Josef {Diblík} and Hana {Halfarová} and Jan {Šafařík}",
  title="Formulas   for   the   general   solution   of   weakly   delayed   planar  linear   discrete   systems   with   constant   coefficients   and   their  analysis",
  annote="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.",
  address="Elsevier",
  chapter="157258",
  doi="10.1016/j.amc.2019.03.068",
  institution="Elsevier",
  number="10",
  volume="358",
  year="2019",
  month="october",
  pages="363--381",
  publisher="Elsevier",
  type="journal article in Web of Science"
}