Lyapunov functions for fractional order systems

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

doi:10.1016/j.cnsns.2014.01.022

Lyapunov functions for fractional order systems

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

University of Chile
University of Chile

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

1416 Scopus citations

Abstract

A new lemma for the Caputo fractional derivatives, when 0. <. α. <. 1, is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.

Original language	English
Pages (from-to)	2951-2957
Number of pages	7
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	19
Issue number	9
DOIs	https://doi.org/10.1016/j.cnsns.2014.01.022
State	Published - Sep 2014
Externally published	Yes

Keywords

Fractional calculus
Fractional-order Lyapunov direct method
Stability of fractional order systems

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10.1016/j.cnsns.2014.01.022

Cite this

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title = "Lyapunov functions for fractional order systems",

abstract = "A new lemma for the Caputo fractional derivatives, when 0. <. α. <. 1, is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.",

keywords = "Fractional calculus, Fractional-order Lyapunov direct method, Stability of fractional order systems",

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

year = "2014",

month = sep,

doi = "10.1016/j.cnsns.2014.01.022",

language = "English",

volume = "19",

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journal = "Communications in Nonlinear Science and Numerical Simulation",

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T1 - Lyapunov functions for fractional order systems

AU - Aguila-Camacho, Norelys

AU - Duarte-Mermoud, Manuel A.

AU - Gallegos, Javier A.

PY - 2014/9

Y1 - 2014/9

N2 - A new lemma for the Caputo fractional derivatives, when 0. <. α. <. 1, is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.

AB - A new lemma for the Caputo fractional derivatives, when 0. <. α. <. 1, is proposed in this paper. This result has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.

KW - Fractional calculus

KW - Fractional-order Lyapunov direct method

KW - Stability of fractional order systems

UR - https://www.scopus.com/pages/publications/84897050571

U2 - 10.1016/j.cnsns.2014.01.022

DO - 10.1016/j.cnsns.2014.01.022

M3 - Article

AN - SCOPUS:84897050571

SN - 1007-5704

VL - 19

SP - 2951

EP - 2957

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 9

ER -

Lyapunov functions for fractional order systems

Abstract

Keywords

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