Consensus of Multiagent Systems Described by Various Noninteger Derivatives

In this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems. These differ by being modeled with one of the following fractional derivatives: the Caputo derivative, the Cap...

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Main Authors: G. Nava-Antonio, G. Fernández-Anaya, E. G. Hernández-Martínez, J. J. Flores-Godoy, E. D. Ferreira-Vázquez
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/3297410
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author G. Nava-Antonio
G. Fernández-Anaya
E. G. Hernández-Martínez
J. J. Flores-Godoy
E. D. Ferreira-Vázquez
author_facet G. Nava-Antonio
G. Fernández-Anaya
E. G. Hernández-Martínez
J. J. Flores-Godoy
E. D. Ferreira-Vázquez
author_sort G. Nava-Antonio
collection DOAJ
description In this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems. These differ by being modeled with one of the following fractional derivatives: the Caputo derivative, the Caputo distributed order derivative, the variable order derivative, the conformable derivative, the local fractional derivative, or the distributed order conformable derivative (the latter defined in this work). Additionally, we apply these results to study the consensus of a fractional multiagent system, considering all of the aforementioned fractional operators. Our analysis covers multiagent systems with linear and nonlinear dynamics, affected by bounded external disturbances and described by fixed directed graphs. Lastly, examples, which are solved analytically and numerically, are presented to validate our contributions.
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institution OA Journals
issn 1076-2787
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language English
publishDate 2019-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-00eb72e19af9424aa125d3643ce701b42025-08-20T02:02:48ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/32974103297410Consensus of Multiagent Systems Described by Various Noninteger DerivativesG. Nava-Antonio0G. Fernández-Anaya1E. G. Hernández-Martínez2J. J. Flores-Godoy3E. D. Ferreira-Vázquez4Departamento de Física y Matemáticas, Universidad Iberoamericana, México City, MexicoDepartamento de Física y Matemáticas, Universidad Iberoamericana, México City, MexicoDepartamento de Estudios en Ingeniería para la Innovación, Universidad Iberoamericana, México City, MexicoDepartamento de Matemática, Universidad Católica del Uruguay, Montevideo, UruguayDepartamento de Ingeniería Eléctrica, Universidad Católica del Uruguay, Montevideo, UruguayIn this paper, we unify and extend recent developments in Lyapunov stability theory to present techniques to determine the asymptotic stability of six types of fractional dynamical systems. These differ by being modeled with one of the following fractional derivatives: the Caputo derivative, the Caputo distributed order derivative, the variable order derivative, the conformable derivative, the local fractional derivative, or the distributed order conformable derivative (the latter defined in this work). Additionally, we apply these results to study the consensus of a fractional multiagent system, considering all of the aforementioned fractional operators. Our analysis covers multiagent systems with linear and nonlinear dynamics, affected by bounded external disturbances and described by fixed directed graphs. Lastly, examples, which are solved analytically and numerically, are presented to validate our contributions.http://dx.doi.org/10.1155/2019/3297410
spellingShingle G. Nava-Antonio
G. Fernández-Anaya
E. G. Hernández-Martínez
J. J. Flores-Godoy
E. D. Ferreira-Vázquez
Consensus of Multiagent Systems Described by Various Noninteger Derivatives
Complexity
title Consensus of Multiagent Systems Described by Various Noninteger Derivatives
title_full Consensus of Multiagent Systems Described by Various Noninteger Derivatives
title_fullStr Consensus of Multiagent Systems Described by Various Noninteger Derivatives
title_full_unstemmed Consensus of Multiagent Systems Described by Various Noninteger Derivatives
title_short Consensus of Multiagent Systems Described by Various Noninteger Derivatives
title_sort consensus of multiagent systems described by various noninteger derivatives
url http://dx.doi.org/10.1155/2019/3297410
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