Stability analysis on a class of nonlinear fractional-order systems

被引：40

作者：

Wang, Zhiliang ^{[1
]}

Yang, Dongsheng ^{[1
]}

Zhang, Huaguang ^{[1
]}

机构：

[1] Northeastern Univ, Sch Informat Sci & Engn, Shenyang 110004, Peoples R China

来源：

NONLINEAR DYNAMICS | 2016年 / 86卷 / 02期

关键词：

Fractional-order; Incommensurate; Comparison inequality; Linearization; Stability; Stabilization; LYAPUNOV FUNCTIONS; PERIODIC-SOLUTIONS; DYNAMICAL-SYSTEMS; NONEXISTENCE; THEOREM;

D O I：

10.1007/s11071-016-2943-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The stability of a class of commensurate and incommensurate nonlinear fractional-order systems is studied. First, two comparison inequalities for incommensurate fractional-order systems are proposed. Based on that, a stability criterion regarding a class of incommensurate fractional-order system is given. And then, three stability criteria are presented concerning a typical class of commensurate nonlinear fractional-order systems. After that, two global stability criteria concerning commensurate and incommensurate nonlinear fractional-order systems are provided, respectively. Finally, the fractional-order Liu system and the fractional-order Chen system are taken as examples to show how to apply the proposed results to stabilization problems.

引用

页码：1023 / 1033

页数：11

共 37 条

[11]

Deng WH, 2007, NONLINEAR DYNAM, V48, P409, DOI [10.1007/s11071-006-9094-0, 10.1007/s11071 -006-9094-0]

[12] Smoothness and stability of the solutions for nonlinear fractional differential equations [J].

Deng, Weihua .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) :1768-1777

[13] 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

[14] Chaotic dynamics of the fractional Lorenz system [J].

Grigorenko, I ;

Grigorenko, E .

PHYSICAL REVIEW LETTERS, 2003, 91 (03)

[15]

Horn RA., 2013, MATRIX ANAL

[16] Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays [J].

Kaczorek, T. .

TRANSNAV-INTERNATIONAL JOURNAL ON MARINE NAVIGATION AND SAFETY OF SEA TRANSPORTATION, 2013, 7 (02) :211-215

[17] Positive fractional linear electrical circuits [J].

Kaczorek, Tadeusz .

PHOTONICS APPLICATIONS IN ASTRONOMY, COMMUNICATIONS, INDUSTRY, AND HIGH-ENERGY PHYSICS EXPERIMENTS 2013, 2013, 8903

[18] PRACTICAL STABILITY AND ASYMPTOTIC STABILITY OF POSITIVE FRACTIONAL 2D LINEAR SYSTEMS [J].

Kaczorek, Tadeusz .

ASIAN JOURNAL OF CONTROL, 2010, 12 (02) :200-207

[19] Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions [J].

Kaslik, Eva ;

Sivasundaram, Seenith .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (03) :1489-1497

[20] Fractional dynamical system and its linearization theorem [J].

Li, Changpin ;

Ma, Yutian .

NONLINEAR DYNAMICS, 2013, 71 (04) :621-633

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