Publication detail

Asymptotic Behavior of the Delayed Matrix Exponential Function

SVOBODA, Z. DIBLÍK, J.

Original Title

Asymptotic Behavior of the Delayed Matrix Exponential Function

English Title

Asymptotic Behavior of the Delayed Matrix Exponential Function

Type

conference paper

Language

en

Original Abstract

The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.

English abstract

The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.

Keywords

asymptotic behavior; delayed matrix exponential; delayed matrix sine; delayed matrix cosine; Lambert function

Released

21.07.2018

Publisher

American Institute of Physics

Location

AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA

ISBN

978-0-7354-1690-1

Book

INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)

Pages from

430006-1

Pages to

430006-4

Pages count

4

URL

Documents

BibTex


@inproceedings{BUT150437,
  author="Zdeněk {Svoboda} and Josef {Diblík}",
  title="Asymptotic Behavior of the Delayed Matrix Exponential Function",
  annote="The paper discusses asymptotic behaviors of the delayed matrix exponential, delayed matrix sine and delayed matrix
cosine. Such functions were defined in connection with a formalization of the step method for linear systems of differential equations with a constant delay r. The above matrix functions are defined by matrix polynomials on every interval [(k − 1)τ, kτ), where k = 0, 1, . . . and τ > 0. To investigate the asymptotic behavior of the delayed matrix functions, the main branch of the Lambert function is used.",
  address="American Institute of Physics",
  booktitle="INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017)",
  chapter="150437",
  doi="10.1063/1.5044021",
  howpublished="online",
  institution="American Institute of Physics",
  year="2018",
  month="july",
  pages="430006-1--430006-4",
  publisher="American Institute of Physics",
  type="conference paper"
}