Publication detail

Exact versus discretized stability regions for a linear delay differential equation

ČERMÁK, J. JÁNSKÝ, J. NECHVÁTAL, L.

Original Title

Exact versus discretized stability regions for a linear delay differential equation

English Title

Exact versus discretized stability regions for a linear delay differential equation

Type

journal article in Web of Science

Language

en

Original Abstract

The paper introduces a system of necessary and sufficient stability conditions for a four- term linear delay difference equation with complex coefficients. These conditions are de- rived explicitly with respect to the time lag and can be viewed as a direct discrete coun- terpart to the existing stability results for the underlying delay differential equation. As a main proof tool, the boundary locus technique combined with some special results of the polynomial theory is employed. Since the studied difference equation serves as a θ - method discretization of its continuous pattern, several problems of numerical stability are discussed as well.

English abstract

The paper introduces a system of necessary and sufficient stability conditions for a four- term linear delay difference equation with complex coefficients. These conditions are de- rived explicitly with respect to the time lag and can be viewed as a direct discrete coun- terpart to the existing stability results for the underlying delay differential equation. As a main proof tool, the boundary locus technique combined with some special results of the polynomial theory is employed. Since the studied difference equation serves as a θ - method discretization of its continuous pattern, several problems of numerical stability are discussed as well.

Keywords

Linear delay difference equation; Linear delay differential equation; θ -method discretization; Exact and numerical stability

Released

15.04.2019

Publisher

Elsevier Science Inc.

Location

New York, USA

Pages from

712

Pages to

722

Pages count

11

URL

Documents

BibTex


@article{BUT155747,
  author="Jan {Čermák} and Jiří {Jánský} and Luděk {Nechvátal}",
  title="Exact versus discretized stability regions for a linear delay differential equation",
  annote="The paper introduces a system of necessary and sufficient stability conditions for a four-
term linear delay difference equation with complex coefficients. These conditions are de-
rived explicitly with respect to the time lag and can be viewed as a direct discrete coun-
terpart to the existing stability results for the underlying delay differential equation. As
a main proof tool, the boundary locus technique combined with some special results of
the polynomial theory is employed. Since the studied difference equation serves as a θ -
method discretization of its continuous pattern, several problems of numerical stability
are discussed as well.",
  address="Elsevier Science Inc.",
  chapter="155747",
  doi="10.1016/j.amc.2018.11.026",
  howpublished="print",
  institution="Elsevier Science Inc.",
  number="1",
  volume="347",
  year="2019",
  month="april",
  pages="712--722",
  publisher="Elsevier Science Inc.",
  type="journal article in Web of Science"
}