On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems

被引：13

作者：

Naifar, Omar ^{[1
]}

Ben Makhlouf, Abdellatif ^{[2
,3
]}

机构：

[1] Sfax Univ, Natl Sch Engn, Control & Energy Management Lab, Sfax, Tunisia

[2] Jouf Univ, Coll Sci, Dept Math, Sakaka, Aljouf, Saudi Arabia

[3] Sfax Univ, Fac Sci Sfax, Dept Math, Sfax, Tunisia

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2021年 / 2021卷

关键词：

ROBUST STABILITY; DIFFERENTIAL-EQUATIONS; UNCERTAIN SYSTEMS; STABILIZABILITY;

D O I：

10.1155/2021/6699756

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, the problem of stabilization and observer design of parameter-dependent perturbed fractional-order systems is investigated. Sufficient conditions on the practical Mittag-Leffler and Mittag-Leffler stability are given based on the Lyapunov technique. Firstly, the problem of stabilization using the state feedback is developed. Secondly, under some sufficient hypotheses, an observer design which provides an estimation of the state is constructed. Finally, numerical examples are provided to validate the contributed results.

引用

页数：6

共 27 条

[1] A priori estimates for solutions of boundary value problems for fractional-order equations [J].

Alikhanov, A. A. .

DIFFERENTIAL EQUATIONS, 2010, 46 (05) :660-666

[2]

[Anonymous], 2006, Theory and Applications of Fractional Differential Equations, DOI DOI 10.1016/S0304-0208(06)80001-0

[3] NECESSARY AND SUFFICIENT CONDITIONS FOR QUADRATIC STABILIZABILITY OF AN UNCERTAIN SYSTEM [J].

BARMISH, BR .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1985, 46 (04) :399-408

[4] STABILITY OF FRACTIONAL-ORDER NONLINEAR SYSTEMS DEPENDING ON A PARAMETER [J].

Ben Makhlouf, Abdellatif ;

Hammami, Mohamed Ali ;

Sioud, Khaled .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2017, 54 (04) :1309-1321

[5] A new Lyapunov function for stability of time-varying nonlinear perturbed systems [J].

BenAbdallah, Abdallah ;

Dlala, Mohsen ;

Hammami, Mohamed Ali .

SYSTEMS & CONTROL LETTERS, 2007, 56 (03) :179-187

[6]

Boyd S., 1994, LINEAR MATRIX INEQUA

[7] Stability and Stabilization for Polytopic LPV Systems with Parameter-Varying Time Delays [J].

Chen, Fu ;

Kang, Shugui ;

Li, Fangyuan .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2019, 2019

[8] Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties [J].

Chen, Liping ;

Wu, Ranchao ;

He, Yigang ;

Yin, Lisheng .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 :274-284

[9] LYAPUNOV FUNCTIONS FOR UNCERTAIN SYSTEMS WITH APPLICATIONS TO THE STABILITY OF TIME-VARYING SYSTEMS [J].

DASGUPTA, S ;

CHOCKALINGAM, G ;

ANDERSON, BDO ;

FU, MY .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1994, 41 (02) :93-106

[10] Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type [J].

Diethelm, Kai .

ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS: AN APPLICATION-ORIENTED EXPOSITION USING DIFFERENTIAL OPERATORS OF CAPUTO TYPE, 2010, 2004 :3-+

← 1 2 3 →