Observer-based controller design for uncertain singular fractional-order systems via LMI approach

2018 ◽  
Author(s):  
Xuefeng Zhang ◽  
Yuanwei Lv ◽  
Linghui Long
Keyword(s):  
Fractional Order ◽  
Controller Design ◽  
Fractional Order Systems ◽  
Lmi Approach

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.

Research on identification of irrational fractional-order systems in frequency domain based on optimization algorithm

2019 ◽  
Vol 41 (15) ◽  
pp. 4351-4357
Author(s):  
Chen Lanfeng ◽  
Xue Dingyu
Keyword(s):  
Frequency Domain ◽  
Fractional Order ◽  
Optimization Algorithm ◽  
Controller Design ◽  
Order System ◽  
Model Parameters ◽  
Fractional Order Systems ◽  
Convolution Integral ◽  
Fractional Order Calculus ◽  
Frequency Domain Response

Fractional-order calculus can obtain better results than the integer-order in control theory, so it has become a research hotspot in recent years. However, the structure of the irrational fractional-order system is complex, so its theoretical analysis and controller design are more difficult. In this paper, a method based on convolution integral is proposed to obtain the frequency domain response of the irrational model. Combined with the optimization algorithm, the model parameters are identified. Moreover, the rationalization of the irrational model is realized, which facilitates the analysis and application design of this kind models. Finally, two examples are given to illustrate the effectiveness and feasibility of the method by identifying parameters and rationalization.

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.

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