Pseudo-state feedback stabilization of commensurate fractional order systems

Automatica ◽  
2010 ◽  
Vol 46 (10) ◽  
pp. 1730-1734 ◽  
Author(s):  
Christophe Farges ◽  
Mathieu Moze ◽  
Jocelyn Sabatier
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
Feedback Stabilization ◽  
Fractional Order Systems

scholarly journals H∞ state feedback control of commensurate fractional order systems

2013 ◽  
Vol 46 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Lamine Fadiga ◽  
Jocelyn Sabatier ◽  
Christophe Farges
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback ◽  
State Feedback Control ◽  
Fractional Order Systems

Stability of Nonlinear Fractional-Order Time Varying Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Sunhua Huang ◽  
Runfan Zhang ◽  
Diyi Chen
Keyword(s):  
Laplace Transform ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Local Stability ◽  
State Feedback ◽  
Sufficient Condition ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Time Varying Systems ◽  
The Stability

This paper is concerned with the stability of nonlinear fractional-order time varying systems with Caputo derivative. By using Laplace transform, Mittag-Leffler function, and the Gronwall inequality, the sufficient condition that ensures local stability of fractional-order systems with fractional order α : 0<α≤1 and 1<α<2 is proposed, respectively. Moreover, the condition of the stability of fractional-order systems with a state-feedback controller is been put forward. Finally, a numerical example is presented to show the validity and feasibility of the proposed method.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Omar Naifar ◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fractional Order ◽  
State Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
Parameter Dependent ◽  
Lyapunov Technique

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.

scholarly journals Dynamic Output Feedback Stabilization of Singular Fractional-Order Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Yanchai Liu ◽  
Liu Cui ◽  
Dengping Duan
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Feedback Stabilization ◽  
Order System ◽  
Dynamic Output Feedback ◽  
Fractional Order Systems ◽  
Stabilizing Controllers ◽  
Dynamic Output ◽  
Dynamic Output Feedback Controller ◽  
The Stability

This paper is concerned with dynamic output feedback controller (DOFC) design problem for singular fractional-order systems with the fractional-orderαsatisfying0<α<2. Based on the stability theory of fractional-order system, sufficient and necessary conditions are derived for the admissibility of the systems, which are more convenient to analytical design of stabilizing controllers than the existing results. A full-order DOFC is then synthesized based on the obtained conditions and the characteristics of Moore-Penrose inverse. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

THE CONTROLLER DESIGN FOR SINGULAR FRACTIONAL-ORDER SYSTEMS WITH FRACTIONAL ORDER 0 <α< 1

2018 ◽  
Vol 60 (2) ◽  
pp. 230-248
Author(s):  
T. ZHAN ◽  
S. P. MA
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary Condition ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Fractional Order Systems ◽  
Static Output

We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order $\unicode[STIX]{x1D6FC}$ when $0<\unicode[STIX]{x1D6FC}<1$. All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example.

Sign in / Sign up

Export Citation Format

Share Document