Stability analysis of linear fractional differential system with multiple time delays

doi:10.1007/s11071-006-9094-0

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	Stability analysis of linear fractional differential system with multiple time delays
	Deng, WH(邓伟华); Li, CP; Lu, JH; Li, CP (reprint author), Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.
ESI NOTE	2017-07-19;Highly Cited Papers
	2007-06
Source Publication	NONLINEAR DYNAMICS
ISSN	0924-090X
Volume	48 Issue:4 Pages:409-416
Abstract	In this paper, we study the stability of n-dimensional linear fractional differential equation with time delays, where the delay matrix is defined in (R+)(nxn). By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. As its an application, we apply our theorem to the delayed system in one spatial dimension studied by Chen and Moore [Nonlinear Dynamics 29, 2002, 191] and determine the asymptotically stable region of the system. We also deal with synchronization between the coupled Duffing oscillators with time delays by the linear feedback control method and the aid of our theorem, where the domain of the control-synchronization parameters is determined.
Keyword	delay Duffing oscillator linear fractional differential system stability synchronization
Subject Area	Engineering ; Mechanics
Publisher	SPRINGER
DOI	10.1007/s11071-006-9094-0
Publication Place	DORDRECHT
Indexed By	SCIE ; EI ; ESI
Language	英语
First Inst	否
WOS ID	WOS:000244837200005
Subtype	Article
EI ID	20071210494516
Department	Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China; Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China; Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100080, Peoples R China
Citation statistics	Cited Times:570[WOS] [WOS Record] [Related Records in WOS]
Document Type	期刊论文
Identifier	https://ir.lzu.edu.cn/handle/262010/117899
Collection	数学与统计学院
Corresponding Author	Li, CP (reprint author), Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China.
Recommended Citation GB/T 7714	Deng, WH,Li, CP,Lu, JH,et al. Stability analysis of linear fractional differential system with multiple time delays[J]. NONLINEAR DYNAMICS,2007,48(4):409-416.
APA	Deng, WH,Li, CP,Lu, JH,&Li, CP .(2007).Stability analysis of linear fractional differential system with multiple time delays.NONLINEAR DYNAMICS,48(4),409-416.
MLA	Deng, WH,et al."Stability analysis of linear fractional differential system with multiple time delays".NONLINEAR DYNAMICS 48.4(2007):409-416.

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