Publication detail
Delay-dependent stability switches in fractional differential equations
KISELA, T. ČERMÁK, J.
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 in English
Fractional delay differential equation; Stability switch; Asymptotic behaviour; Stabilization
Released
01.12.2019
Publisher
Elsevier
Location
RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS
ISSN
1007-5704
Volume
79
Number
1
Pages from–to
1–19
Pages count
19
BIBTEX
@article{BUT159358,
author="Tomáš {Kisela} and Jan {Čermák},
title="Delay-dependent stability switches in fractional differential equations",
year="2019",
volume="79",
number="1",
month="December",
pages="1--19",
publisher="Elsevier",
address="RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS",
issn="1007-5704"
}