On fractional extensions of Barbalat Lemma

Javier A. Gallegos; Manuel A. Duarte-Mermoud; Norelys Aguila-Camacho; Rafael Castro-Linares

doi:10.1016/j.sysconle.2015.07.004

On fractional extensions of Barbalat Lemma

Javier A. Gallegos
, Manuel A. Duarte-Mermoud
, Norelys Aguila-Camacho
, Rafael Castro-Linares

Research output: Contribution to journal › Article › peer-review

70 Scopus citations

Abstract

This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory.

Original language	English
Pages (from-to)	7-12
Number of pages	6
Journal	Systems and Control Letters
Volume	84
DOIs	https://doi.org/10.1016/j.sysconle.2015.07.004
State	Published - 11 Aug 2015
Externally published	Yes

Keywords

Asymptotics properties
Barbalat Lemma
Fractional calculus

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10.1016/j.sysconle.2015.07.004

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title = "On fractional extensions of Barbalat Lemma",

abstract = "This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory.",

keywords = "Asymptotics properties, Barbalat Lemma, Fractional calculus",

author = "Gallegos, \{Javier A.\} and Duarte-Mermoud, \{Manuel A.\} and Norelys Aguila-Camacho and Rafael Castro-Linares",

year = "2015",

month = aug,

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doi = "10.1016/j.sysconle.2015.07.004",

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AU - Gallegos, Javier A.

AU - Duarte-Mermoud, Manuel A.

AU - Aguila-Camacho, Norelys

AU - Castro-Linares, Rafael

PY - 2015/8/11

Y1 - 2015/8/11

N2 - This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory.

AB - This paper presents Barbalat-like lemmas for fractional order integrals, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral. Some examples in the context of asymptotic behaviour of solutions of fractional order differential equations, indicate the potential application of these lemmas in control theory.

KW - Asymptotics properties

KW - Barbalat Lemma

KW - Fractional calculus

UR - https://www.scopus.com/pages/publications/84938848802

U2 - 10.1016/j.sysconle.2015.07.004

DO - 10.1016/j.sysconle.2015.07.004

M3 - Article

AN - SCOPUS:84938848802

SN - 0167-6911

VL - 84

SP - 7

EP - 12

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

On fractional extensions of Barbalat Lemma

Abstract

Keywords

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