Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative

Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative

Abstract In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix theory we give a necessary and sufficient stability condition and some brief suffi...

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Main Authors: Hong Li, Shou-ming Zhong, Jun Cheng, Hou-biao Li
Format: Article
Language:English
Published: SpringerOpen 2019-03-01
Series:Advances in Difference Equations
Subjects:
Fractional system
Stability
Laplace transform
Fractional derivative
Online Access:http://link.springer.com/article/10.1186/s13662-019-2024-5
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spelling doaj-7d0d356dd973478c9ade5fadd7f3d0382020-11-25T01:48:44ZengSpringerOpenAdvances in Difference Equations1687-18472019-03-01201911810.1186/s13662-019-2024-5Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivativeHong Li0Shou-ming Zhong1Jun Cheng2Hou-biao Li3School of Mathematical Sciences, University of Electronic Science and Technology of ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of ChinaQingdao University of Science and TechnologySchool of Mathematical Sciences, University of Electronic Science and Technology of ChinaAbstract In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix theory we give a necessary and sufficient stability condition and some brief sufficient stability conditions. The proposed method is quite different from the other in the literature. In addition, we provide some examples to demonstrate the effectiveness of our results.http://link.springer.com/article/10.1186/s13662-019-2024-5Fractional systemStabilityLaplace transformFractional derivative
collection DOAJ
language English
format Article
sources DOAJ
author Hong Li
Shou-ming Zhong
Jun Cheng
Hou-biao Li
spellingShingle Hong Li
Shou-ming Zhong
Jun Cheng
Hou-biao Li
Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative
Advances in Difference Equations
Fractional system
Stability
Laplace transform
Fractional derivative
author_facet Hong Li
Shou-ming Zhong
Jun Cheng
Hou-biao Li
author_sort Hong Li
title Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative
title_short Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative
title_full Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative
title_fullStr Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative
title_full_unstemmed Stability analysis of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative
title_sort stability analysis of fractional-order linear system with time delay described by the caputo–fabrizio derivative
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2019-03-01
description Abstract In this paper, we define a characteristic equation of fractional-order linear system with time delay described by the Caputo–Fabrizio derivative. At the same time, by applying the Laplace transform and matrix theory we give a necessary and sufficient stability condition and some brief sufficient stability conditions. The proposed method is quite different from the other in the literature. In addition, we provide some examples to demonstrate the effectiveness of our results.
topic Fractional system
Stability
Laplace transform
Fractional derivative
url http://link.springer.com/article/10.1186/s13662-019-2024-5
work_keys_str_mv AT hongli stabilityanalysisoffractionalorderlinearsystemwithtimedelaydescribedbythecaputofabrizioderivative
AT shoumingzhong stabilityanalysisoffractionalorderlinearsystemwithtimedelaydescribedbythecaputofabrizioderivative
AT juncheng stabilityanalysisoffractionalorderlinearsystemwithtimedelaydescribedbythecaputofabrizioderivative
AT houbiaoli stabilityanalysisoffractionalorderlinearsystemwithtimedelaydescribedbythecaputofabrizioderivative
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