Publication detail

Explicit stability conditions for a linear trinomial delay difference equation

ČERMÁK, J. JÁNSKÝ, J.

Original Title

Explicit stability conditions for a linear trinomial delay difference equation

English Title

Explicit stability conditions for a linear trinomial delay difference equation

Type

journal article in Web of Science

Language

en

Original Abstract

The paper presents a new type of necessary and sufficient conditions for the asymptotic stability of the zero solution of the linear trinomial difference equation with two delays. Compared to the existing criteria, our conditions are fully explicit and simple to analyse. In particular, we show the usefulness of these conditions in the description of appropriate stability sets for the studied difference equation with fixed delays as well as with fixed coefficients. As a by-product, we obtain an explicit criterion guaranteeing that all the zeros of the general three-term polynomial are located inside the unit circle in the complex plane.

English abstract

The paper presents a new type of necessary and sufficient conditions for the asymptotic stability of the zero solution of the linear trinomial difference equation with two delays. Compared to the existing criteria, our conditions are fully explicit and simple to analyse. In particular, we show the usefulness of these conditions in the description of appropriate stability sets for the studied difference equation with fixed delays as well as with fixed coefficients. As a by-product, we obtain an explicit criterion guaranteeing that all the zeros of the general three-term polynomial are located inside the unit circle in the complex plane.

Keywords

Linear delay difference equation; asymptotic stability; characteristic polynomial

RIV year

2015

Released

01.05.2015

Publisher

Elsevier

Pages from

56

Pages to

60

Pages count

5

Documents

BibTex


@article{BUT110776,
  author="Jan {Čermák} and Jiří {Jánský}",
  title="Explicit stability conditions for a linear trinomial delay difference equation",
  annote="The paper presents a new type of necessary and sufficient conditions for the asymptotic stability of the zero solution of the linear trinomial difference equation with two delays.  Compared to the existing criteria, our conditions are fully explicit and simple to analyse. In particular, we show the usefulness of these conditions in the description of appropriate stability sets for the studied difference equation with fixed delays as well as with fixed coefficients. As a by-product, we obtain an explicit criterion guaranteeing that all the zeros of the general three-term polynomial are located inside the unit circle in the complex plane.",
  address="Elsevier",
  chapter="110776",
  doi="10.1016/j.aml.2014.11.014",
  institution="Elsevier",
  number="5",
  volume="43",
  year="2015",
  month="may",
  pages="56--60",
  publisher="Elsevier",
  type="journal article in Web of Science"
}