Stabilization of impulsive fractional-order dynamic systems involving the Caputo fractional derivative of variable-order via a linear feedback controller

被引：20

作者：

Duc, Tran Minh ^{[1
]}

Van Hoa, Ngo ^{[2
,3
]}

机构：

[1] Thu Dau Mot Univ, Inst Engn & Technol, Binh Duong, Vietnam

[2] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam

[3] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

来源：

CHAOS SOLITONS & FRACTALS | 2021年 / 153卷

关键词：

The generalized Caputo fractional derivative; Variable-order fractional modeling; Mittag-Leffler stability; Variable-order fractional Lyapunov approach; LYAPUNOV FUNCTIONS; STABILITY ANALYSIS; EXISTENCE;

D O I：

10.1016/j.chaos.2021.111525

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates the stability and stabilization problem of variable-order fractional nonlinear dynamic systems with impulsive effects (VO-IFNDS) via a linear feedback controller. New inequalities on the VO Caputo fractional derivatives are established in this paper, which plays an essential role in the study of the stability theory of VO-IFNDS. Based on utilizing S-procedure and analytical technique, several sufficient criteria on Mittag-Leffler stability and asymptotical stability of VO-IFNDS are presented by means of the extension of the Lyapunov direct method. Finally, numerical examples are given to show the efficiency of the proposed method. (c) 2021 Elsevier Ltd. All rights reserved.

引用

页数：16

共 35 条

[1] Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel [J].

Abdeljawad, Thabet ;

Baleanu, Dumitru .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (03) :1098-1107

[2] Fractional economic models based on market equilibrium in the frame of different type kernelsn [J].

Acay, Bahar ;

Bas, Erdal ;

Abdeljawad, Thabet .

CHAOS SOLITONS & FRACTALS, 2020, 130

[3] 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

[4] Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications [J].

Al-Smadi, Mohammed ;

Abu Arqub, Omar ;

Zeidan, Dia .

CHAOS SOLITONS & FRACTALS, 2021, 146 (146)

[5] NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model [J].

Atangana, Abdon ;

Baleanu, Dumitru .

THERMAL SCIENCE, 2016, 20 (02) :763-769

[6] On some new properties of fractional derivatives with Mittag-Leffler kernel [J].

Baleanu, Dumitru ;

Fernandez, Arran .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 59 :444-462

[7] Numerically pricing double barrier options in a time-fractional Black-Scholes model [J].

De Staelen, R. H. ;

Hendy, A. S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (06) :1166-1175

[8] 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

[9] Chaotic analysis of Atangana-Baleanu derivative fractional order Willis aneurysm system [J].

Gao, Fei ;

Li, Wen-Qin ;

Tong, Heng-Qing ;

Li, Xi-Ling .

CHINESE PHYSICS B, 2019, 28 (09)

[10] A comment on some new definitions of fractional derivative [J].

Giusti, Andrea .

NONLINEAR DYNAMICS, 2018, 93 (03) :1757-1763

← 1 2 3 4 →