Publication detail

Delay-dependent stability switches in fractional differential equations

KISELA, T. ČERMÁK, J.

Original Title

Delay-dependent stability switches in fractional differential equations

English Title

Delay-dependent stability switches in fractional differential equations

Type

journal article in Web of Science

Language

en

Original Abstract

This paper discusses stability properties of a linear fractional delay differential system involving both delayed as well as non-delayed terms. As a main result, the explicit stability dependence on a changing time delay is described, including conditions for the appearance, number and exact calculations of stability switches for this system when its stability property turns into instability and vice versa in view of a monotonically increasing lag. Some supporting asymptotic results are stated as well. The proof technique is based on analysis of the generalized delay exponential function of the Mittag-Leffler type combined with D-decomposition method. The obtained results are illustrated via a fractional Lotka-Volterra population model and applied to a stabilization problem of the control theory.

English abstract

This paper discusses stability properties of a linear fractional delay differential system involving both delayed as well as non-delayed terms. As a main result, the explicit stability dependence on a changing time delay is described, including conditions for the appearance, number and exact calculations of stability switches for this system when its stability property turns into instability and vice versa in view of a monotonically increasing lag. Some supporting asymptotic results are stated as well. The proof technique is based on analysis of the generalized delay exponential function of the Mittag-Leffler type combined with D-decomposition method. The obtained results are illustrated via a fractional Lotka-Volterra population model and applied to a stabilization problem of the control theory.

Keywords

Fractional delay differential equation; Stability switch; Asymptotic behaviour; Stabilization

Released

01.12.2019

Publisher

Elsevier

Location

RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS

Pages from

1

Pages to

19

Pages count

19

URL

Documents

BibTex


@article{BUT159358,
  author="Tomáš {Kisela} and Jan {Čermák}",
  title="Delay-dependent stability switches in fractional differential equations",
  annote="This paper discusses stability properties of a linear fractional delay differential system involving both delayed as well as non-delayed terms. As a main result, the explicit stability dependence on a changing time delay is described, including conditions for the appearance, number and exact calculations of stability switches for this system when its stability property turns into instability and vice versa in view of a monotonically increasing lag. Some supporting asymptotic results are stated as well. The proof technique is based on analysis of the generalized delay exponential function of the Mittag-Leffler type combined with D-decomposition method. The obtained results are illustrated via a fractional Lotka-Volterra population model and applied to a stabilization problem of the control theory.",
  address="Elsevier",
  chapter="159358",
  doi="10.1016/j.cnsns.2019.104888",
  howpublished="print",
  institution="Elsevier",
  number="1",
  volume="79",
  year="2019",
  month="december",
  pages="1--19",
  publisher="Elsevier",
  type="journal article in Web of Science"
}