Necessary and sufficient conditions for the dynamic output feedback stabilization of fractional-order systems with order 0 < α < 1

2019 ◽  
Vol 62 (9) ◽  
Author(s):  
Ying Guo ◽  
Chong Lin ◽  
Bing Chen ◽  
Qingguo Wang
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
Dynamic Output Feedback ◽  
Fractional Order Systems ◽  
Output Feedback Stabilization ◽  
Dynamic Output ◽  
Necessary And Sufficient

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.

scholarly journals Admissibility of Fractional Order Descriptor Systems Based on Complex Variables: An LMI Approach

2020 ◽  
Vol 4 (1) ◽  
pp. 8
Author(s):  
Xuefeng Zhang ◽  
Yuqing Yan
Keyword(s):  
Fractional Order ◽  
Complex Plane ◽  
Sufficient Conditions ◽  
Complex Variables ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
Fractional Order Systems ◽  
Lmi Approach ◽  
Numerical Examples ◽  
Necessary And Sufficient

This paper is devoted to the admissibility issue of singular fractional order systems with order α ∈ ( 0 , 1 ) based on complex variables. Firstly, with regard to admissibility, necessary and sufficient conditions are obtained by strict LMI in complex plane. Then, an observer-based controller is designed to ensure system admissible. Finally, numerical examples are given to reveal the validity of the theoretical conclusions.

scholarly journals New perspectives on output feedback stabilization at an unobservable target

2021 ◽  
Author(s):  
Lucas Brivadis ◽  
Jean-Paul Gauthier ◽  
Ludovic Sacchelli ◽  
Ulysse Serres
Keyword(s):  
Output Feedback ◽  
Ad Hoc ◽  
Feedback Stabilization ◽  
Target Point ◽  
Dynamic Output Feedback ◽  
Infinite Dimensional ◽  
Output Feedback Stabilization ◽  
Dynamic Output ◽  
New Strategy ◽  
Nonlinear Observation

We address the problem of dynamic output feedback stabilization at an unobservable target point. The challenge lies in according the antagonistic nature of the objective and the properties of the system: the system tends to be less observable as it approaches the target. We illustrate two main ideas: well chosen perturbations of a state feedback law can yield new observability properties of the closed-loop system, and embedding systems into bilinear systems admitting observers with dissipative error systems allows to mitigate the observability issues. We apply them on a case of systems with linear dynamics and nonlinear observation map and make use of an ad hoc finite-dimensional embedding. More generally, we introduce a new strategy based on infinite-dimensional unitary embeddings. To do so, we extend the usual definition of dynamic output feedback stabilization in order to allow infinite-dimensional observers fed by the output. We show how this technique, based on representation theory, may be applied to achieve output feedback stabilization at an unobservable target.

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