Publication detail

Exact versus discretized stability regions for a linear delay differential equation

ČERMÁK, J. JÁNSKÝ, J. NECHVÁTAL, L.

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 in English

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

ISSN

0096-3003

Volume

347

Number

1

Pages from–to

712–722

Pages count

11

BIBTEX


@article{BUT155747,
  author="Jan {Čermák} and Jiří {Jánský} and Luděk {Nechvátal},
  title="Exact versus discretized stability regions for a linear delay differential equation",
  year="2019",
  volume="347",
  number="1",
  month="April",
  pages="712--722",
  publisher="Elsevier Science Inc.",
  address="New York, USA",
  issn="0096-3003"
}