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.

scholarly journals Design of Static Output Feedback Controller for Fractional-Order T-S Fuzzy System

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhile Xia
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Matrix Decomposition ◽  
Order Theory ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Feedback Controllers ◽  
Static Output

This paper studies the design of fuzzy static output feedback controllers for two kinds of fractional-order T-S fuzzy systems. The fractional order α satisfies 0<α<1 and 1≤α<2. Based on the fractional order theory, matrix decomposition technique, and projection theorem, four new sufficient conditions for the asymptotic stability of the system and the corresponding controller design methods are given. All the results can be expressed by linear matrix inequalities, and the relationship between fuzzy subsystems is also considered. These have great advantages in solving the results and reducing the conservatism. Finally, a simulation example is given to show the effectiveness of the proposed method.

scholarly journals Robust Admissibilization of Descriptor Systems by Static Output-Feedback: An LMI Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
M. Chaabane ◽  
F. Tadeo ◽  
D. Mehdi ◽  
M. Souissi
Keyword(s):  
Output Feedback ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Initial Value ◽  
Feedback Controllers ◽  
Classical State ◽  
Static Output

The problem of the stabilization of descriptor systems in continuous-time via static output-feedback is studied in this paper and an approach to solve it is proposed. For this, sufficient conditions are derived for the closed-loop system to be admissible (i.e., stable, regular, and impulse-free). These conditions are expressed in terms of a strict Linear Matrix Inequality (LMI); so they are tractable using numerical computations. The proposed controller design methodology is based on two steps: the first is dedicated to synthesizing a classical state-feedback controller, which is used as the initial value for the second step, which uses an LMI problem to obtain static output-feedback controllers that give admissibility. Finally, a numerical example is given to illustrate the results.

scholarly journals Stabilization for Singular Fractional-Order Systems via Static Output Feedback

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 71678-71684 ◽  
Author(s):  
Ying Guo ◽  
Chong Lin ◽  
Bing Chen ◽  
Qing-Guo Wang
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Static Output Feedback ◽  
Fractional Order Systems ◽  
Static Output

Static output feedback stabilization of nonlinear fractional-order glucose-insulin system

2012 ◽  
Author(s):  
Ibrahima N'Doye ◽  
Holger Voos ◽  
Mohamed Darouach ◽  
Jochen G. Schneider ◽  
Nicolas Knauf
Keyword(s):  
Fractional Order ◽  
Output Feedback ◽  
Feedback Stabilization ◽  
Static Output Feedback ◽  
Output Feedback Stabilization ◽  
Static Output

scholarly journals PiecewiseH∞Static Output Feedback Controller Design for Nonlinear Systems Based on T-S Affine Fuzzy Models

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xingang Zhao
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Controller Design ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Output Feedback Controller ◽  
Fuzzy Models ◽  
Complex Nonlinear Systems ◽  
Static Output

This paper is concerned with the problem of designingH∞controllers via static output feedback controller for a class of complex nonlinear systems, which is approximated by continuous-time affine fuzzy models. A decomposition method is presented to divide the output-space into different operating regions and interpolation regions. Based on this partition, a novel piecewise controller with affine terms via static output feedback is designed. By using a dilated linear matrix inequality (LMI) characterization, some nonconvex conditions are converted into convex ones to make the asymptotic stability andH∞performance of the closed-looped system. The effectiveness of the proposed method is illustrated by a numerical example.

scholarly journals Necessary and Sufficient Dissipativity-Based Conditions for Feedback Stabilization

2022 ◽  
Author(s):  
Diego Madeira
Keyword(s):  
Controller Design ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Full State ◽  
Full State Feedback ◽  
Necessary And Sufficient ◽  
Static Output

Using the notion of exponential QSR-dissipativity, this work presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality (LMI) conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach.

Static Output Feedback Stabilization with H∞ Performance for Discrete-Time Piecewise Affine Systems: An LMI Approach

2011 ◽  
Vol 48-49 ◽  
pp. 1112-1115
Author(s):  
Juan Wang ◽  
Tao Zhang
Keyword(s):  
Output Feedback ◽  
Feedback Stabilization ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Convex Optimization Problem ◽  
Closed Loop Systems ◽  
Control Schemes ◽  
The Stability ◽  
Static Output

A static output feedback (SOF) control schemes are proposed. The basic idea of it is to construct piecewise quadratic Lyapunov function and introduce a dissipation inequality to guarantee the system energy dissipation. It is shown that the controller analysis or the synthesis problem can be casted as convex optimization problem, and the controller can be obtained by solving a set of linear matrix inequalities. The designed controllers not only guarantee the stability of the closed-loop systems, but also obtain the disturbance attenuation ability.

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