Output Stabilization of Linear Systems in Given Set

This paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the origi...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-08, Vol.11 (16), p.3542
Main Authors: Nguyen, Ba Huy, Furtat, Igor B.
Format: Article
Language:English
Subjects:
change of coordinates
control
Control systems design
Control theory
Controllers
Coordinate transformations
Design
Euclidean space
Food science
Guarantees
Laws, regulations and rules
linear dynamical system
Linear matrix inequalities
Linear systems
Mathematical analysis
stability
Stabilization
State estimation
State feedback
State observers
State vectors
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Summary:This paper presents a method for designing control laws to achieve output stabilization of linear systems within specified sets, even in the presence of unknown bounded disturbances. The approach consists of two stages. In the first stage, a coordinate transformation is utilized to convert the original system with output constraints into a new system without constraints. In the second stage, a controller is designed to ensure the boundedness of the controlled variable of the transformed system obtained in the first stage. Two distinct control strategies are presented in the second stage, depending on the measurability of the state vector. If the state vector is measurable, a controller is designed using state feedback based on the Lyapunov method and Linear Matrix Inequalities (LMIs). Alternatively, if only the output vector is measurable, an observer-based controller is designed using a Luenberger observer. In this case, the state estimation error does not need to converge to zero but must remain bounded. The efficacy of the proposed method and the validity of the theoretical results are demonstrated through simulations performed in MATLAB/Simulink.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11163542