On fractional extensions of Barbalat Lemma

被引：61

作者：

Gallegos, Javier A. ^{[1
,2
]}

Duarte-Mermoud, Manuel A. ^{[1
,2
]}

Aguila-Camacho, Norelys ^{[1
,2
]}

Castro-Linares, Rafael ^{[3
]}

机构：

[1] Univ Chile, Dept Elect Engn, Santiago, Chile

[2] Univ Chile, Adv Min Technol Ctr, Santiago, Chile

[3] CINVESTAV, Dept Elect Engn, Mexico City 14000, DF, Mexico

来源：

SYSTEMS & CONTROL LETTERS | 2015年 / 84卷

关键词：

Fractional calculus; Asymptotics properties; Barbalat Lemma;

D O I：

10.1016/j.sysconle.2015.07.004

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：7 / 12

页数：6

共 11 条

[1] Lyapunov functions for fractional order systems [J].

Aguila-Camacho, Norelys ;

Duarte-Mermoud, Manuel A. ;

Gallegos, Javier A. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (09) :2951-2957

[2]

[Anonymous], 2006, THEORY APPL FRACTION

[3]

[Anonymous], SCI WORLD J

[4]

Diethelm K., 2004, The analysis of fractional differential equations

[5] A survey on the stability of fractional differential equations [J].

Li, C. P. ;

Zhang, F. R. .

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS, 2011, 193 (01) :27-47

[6] New versions of Barbalat's lemma with applications [J].

Hou M. ;

Duan G. ;

Guo M. .

Journal of Control Theory and Applications, 2010, 8 (4) :545-547

[7]

Narendra K., 2012, STABLE ADAPTIVE SYST

[8]

Samko A. A., 1993, Fractional Integrals andDerivatives: Theory and Applications

[9] Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control [J].

Vinagre, BM ;

Petrás, I ;

Podlubny, I ;

Chen, YQ .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :269-279

[10] Corrections to "Stochastic Barbalat's Lemma and Its Applications" [J].

Yu, Xin ;

Wu, Zhaojing .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2014, 59 (05) :1386-1390

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