On the Lyapunov theory for fractional order systems

被引：81
作者：
Gallegos, Javier A. [1 ,2 ]
Duarte-Mermoud, Manuel A. [1 ,2 ]
机构：
[1] Univ Chile, Dept Elect Engn, Av Tupper Santiago 2007, Santiago, Chile
[2] Univ Chile, Adv Min Technol Ctr, Av Tupper Santiago 2007, Santiago, Chile
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 287卷
关键词：
Lyapunov theory; Fractional order system; Stability; EQUATIONS; STABILITY;
D O I：
10.1016/j.amc.2016.04.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide the main features of Lyapunov theory when it is formulated for fractional order systems. We give consistent extensions of Lyapunov, LaSalle and Chetaev classical theorems to the case of fractional order systems. We give examples to illustrate the applications of the concepts and propositions introduced. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：161 / 170
页数：10
相关论文
共 21 条
  • [1] On Fractional Order Dengue Epidemic Model
    Al-Sulami, Hamed
    El-Shahed, Moustafa
    Nieto, Juan J.
    Shammakh, Wafa
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2014, 2014
  • [2] A priori estimates for solutions of boundary value problems for fractional-order equations
    Alikhanov, A. A.
    [J]. DIFFERENTIAL EQUATIONS, 2010, 46 (05) : 660 - 666
  • [3] [Anonymous], 2006, THEORY APPL FRACTION
  • [4] [Anonymous], 1963, LINEAR SYSTEM THEORY
  • [5] Diethelm K., 2004, The analysis of fractional differential equations
  • [6] Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems
    Duarte-Mermoud, Manuel A.
    Aguila-Camacho, Norelys
    Gallegos, Javier A.
    Castro-Linares, Rafael
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 22 (1-3) : 650 - 659
  • [7] Boundedness and convergence on fractional order systems
    Gallegos, Javier A.
    Duarte-Mermoud, Manuel A.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2016, 296 : 815 - 826
  • [8] On fractional extensions of Barbalat Lemma
    Gallegos, Javier A.
    Duarte-Mermoud, Manuel A.
    Aguila-Camacho, Norelys
    Castro-Linares, Rafael
    [J]. SYSTEMS & CONTROL LETTERS, 2015, 84 : 7 - 12
  • [9] Stability of q-fractional non-autonomous systems
    Jarad, Fahd
    Abdeljawad, Thabet
    Baleanu, Dumitru
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (01) : 780 - 784
  • [10] Lakshmikantham V., 2008, Commun. Appl. Anal., V12, P365
123