Lyapunov stability analysis of fractional nonlinear systems

被引:122
作者
Liu, Song [1 ]
Jiang, Wei [1 ]
Li, Xiaoyan [1 ]
Zhou, Xian-Feng [1 ]
机构
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
关键词
Fractional nonlinear system; Lyapunov direct method; Mittag-Leffler stability; Asymptotical stability; DELAY SYSTEMS; THEOREM;
D O I
10.1016/j.aml.2015.06.018
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Lyapunov direct method provides a very effective approach to analyze stability of nonlinear systems, however, the well-known Leibniz rule is not suitable for fractional derivatives. This paper deals with fractional nonlinear systems and several algebraic criteria of Mittag-Leflier and asymptotical stability are obtained by using S-procedure and analytical technique. Finally, an example is given to show that it is very convenient to check stability of practical systems by using our proposed methods. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码:13 / 19
页数:7
相关论文
共 21 条
[1]   BIBO stability of some classes of delay systems and fractional systems [J].
Abusaksaka, Aolo Bashar ;
Partington, Jonathan R. .
SYSTEMS & CONTROL LETTERS, 2014, 64 :43-46
[2]  
[Anonymous], 2006, THEORY APPL FRACTION
[3]  
[Anonymous], 1993, INTRO FRACTIONAL CA
[4]  
[Anonymous], 1999, FRACTIONAL DIFFERENT
[5]   Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks [J].
Chen, Diyi ;
Zhang, Runfan ;
Liu, Xinzhi ;
Ma, Xiaoyi .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (12) :4105-4121
[6]   New results on stability and stabilization of a class of nonlinear fractional-order systems [J].
Chen, Liping ;
He, Yigang ;
Chai, Yi ;
Wu, Ranchao .
NONLINEAR DYNAMICS, 2014, 75 (04) :633-641
[7]   Analytical stability bound for a class of delayed fractional-order dynamic systems [J].
Chen, YQ ;
Moore, KL .
NONLINEAR DYNAMICS, 2002, 29 (1-4) :191-200
[8]   Existence of solutions of initial value problems for nonlinear fractional differential equations [J].
Deng, Jiqin ;
Deng, Ziming .
APPLIED MATHEMATICS LETTERS, 2014, 32 :6-12
[9]  
Deng WH, 2007, NONLINEAR DYNAM, V48, P409, DOI [10.1007/s11071-006-9094-0, 10.1007/s11071 -006-9094-0]
[10]   Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems [J].
Duarte-Mermoud, Manuel A. ;
Aguila-Camacho, Norelys ;
Gallegos, Javier A. ;
Castro-Linares, Rafael .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 22 (1-3) :650-659