Stability criteria for a class of fractional order systems

被引：18

作者：

Kheirizad, Iraj ^{[1
]}

Tavazoei, Mohammad Saleh ^{[2
]}

Jalali, Ali Akbar ^{[1
]}

机构：

[1] Iran Univ Sci & Technol, Dept Elect Engn, Tehran, Iran

[2] Sharif Univ Technol, Dept Elect Engn, Tehran, Iran

来源：

NONLINEAR DYNAMICS | 2010年 / 61卷 / 1-2期

关键词：

Fractional order system; Stability; Stabilization; DELAY SYSTEMS; STABILIZATION; ALGORITHM; POINTS;

D O I：

10.1007/s11071-009-9638-1

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

This paper deals with the stability problem in LTI fractional order systems having fractional orders between 1 and 1.5. Some sufficient algebraic conditions to guarantee the BIBO stability in such systems are obtained. The obtained conditions directly depend on the coefficients of the system equations, and consequently using them is easier than the use of conditions constructed based on solving the characteristic equation of the system. Some illustrations are presented to show the applicability of the obtained conditions. For example, it is shown that these conditions may be useful in stabilization of unstable fractional order systems or in taming fractional order chaotic systems.

引用

页码：153 / 161

页数：9

共 33 条

[1] Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models [J].

Ahmed, E. ;

El-Sayed, A. M. A. ;

El-Saka, H. A. A. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) :542-553

[2] Necessary and sufficient stability condition of fractional-order interval linear systems [J].

Ahn, Hyo-Sung ;

Chen, YangQuan .

AUTOMATICA, 2008, 44 (11) :2985-2988

[3]

[Anonymous], 2008, 3 IFAC WORKSH FRACT, DOI DOI 10.1016/j.cnsns.2009.05.070

[4] Fractional non-linear modelling of ultracapacitors [J].

Bertrand, Nicolas ;

Sabatier, Jocelyn ;

Briat, Olivier ;

Vinassa, Jean-Michel .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2010, 15 (05) :1327-1337

[5] Coprime factorizations and stability of fractional differential systems [J].

Bonnet, C ;

Partington, JR .

SYSTEMS & CONTROL LETTERS, 2000, 41 (03) :167-174

[6] Stabilization of some fractional delay systems of neutral type [J].

Bonnet, Catherine ;

Partington, Jonathan R. .

AUTOMATICA, 2007, 43 (12) :2047-2053

[7] Robust stability check of fractional order linear time invariant systems with interval uncertainties [J].

Chen, YangQuan ;

Ahn, Hyo-Sung ;

Podlubny, Igor .

SIGNAL PROCESSING, 2006, 86 (10) :2611-2618

[8] 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

[9] Analysis of fractional differential equations with multi-orders [J].

Deng, Weihua ;

Li, Changpin ;

Guo, Qian .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2007, 15 (02) :173-182

[10]

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

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