Publication detail

Linear Difference Weakly Delayed Systems, the Case of Complex Conjugate Eigenvalues of the Matrix of Non-Delayed Terms

ŠAFAŘÍK, J. DIBLÍK, J.

Original Title

Linear Difference Weakly Delayed Systems, the Case of Complex Conjugate Eigenvalues of the Matrix of Non-Delayed Terms

English Title

Linear Difference Weakly Delayed Systems, the Case of Complex Conjugate Eigenvalues of the Matrix of Non-Delayed Terms

Type

conference paper

Language

en

Original Abstract

A linear weakly delayed discrete system with single delay $$x(k+1) = Ax(k) + Bx(k-m),\ k = 0, 1, \dots,$$ in $\mathbb{R}^3$ is considered, where $A$ and $B$ are $3 \times 3$ matrices and $m \geq 1$ is an integer. Assuming that the characteristic equation of the matrix $A$ has a pair of complex conjugate roots, the general solution of the given system is constructed.

English abstract

A linear weakly delayed discrete system with single delay $$x(k+1) = Ax(k) + Bx(k-m),\ k = 0, 1, \dots,$$ in $\mathbb{R}^3$ is considered, where $A$ and $B$ are $3 \times 3$ matrices and $m \geq 1$ is an integer. Assuming that the characteristic equation of the matrix $A$ has a pair of complex conjugate roots, the general solution of the given system is constructed.

Keywords

Discrete system, weakly delayed system, linear system, initial problem, single delay

Released

18.12.2017

Publisher

Univerzita obrany v Brně

Location

Brno

ISBN

978-80-7582-026-6

Book

MITAV 2017 (Matematika, informační technologie a aplikované vědy), Post-conference proceedings of extended versions of selected papers

Edition number

1

Pages from

235

Pages to

247

Pages count

262

URL

Documents

BibTex


@inproceedings{BUT142577,
  author="Jan {Šafařík} and Josef {Diblík}",
  title="Linear Difference Weakly Delayed Systems, the Case of Complex Conjugate Eigenvalues of the Matrix of Non-Delayed Terms",
  annote="A linear weakly delayed discrete system with single delay 
$$x(k+1) = Ax(k) + Bx(k-m),\ k = 0, 1, \dots,$$
in $\mathbb{R}^3$ is considered, where $A$ and $B$ are $3 \times 3$ matrices and $m \geq 1$ is an integer. Assuming that the characteristic equation of the matrix $A$ has a pair of complex conjugate roots, the general solution of the given system is constructed.",
  address="Univerzita obrany v Brně",
  booktitle="MITAV 2017 (Matematika, informační technologie a aplikované vědy), Post-conference proceedings of extended versions of selected papers",
  chapter="142577",
  howpublished="online",
  institution="Univerzita obrany v Brně",
  year="2017",
  month="december",
  pages="235--247",
  publisher="Univerzita obrany v Brně",
  type="conference paper"
}