Stabilization of homogeneous polynomial systems in the plane

Hamadi Jerbi; Thouraya Kharrat; Khaled Sioud

Kybernetika (2016)

  • Volume: 52, Issue: 1, page 131-152
  • ISSN: 0023-5954

Abstract

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In this paper, we study the problem of stabilization via homogeneous feedback of single-input homogeneous polynomial systems in the plane. We give a complete classification of systems for which there exists a homogeneous stabilizing feedback that is smooth on ℝ 2 ∖ { ( 0 , 0 ) } and preserve the homogeneity of the closed loop system. Our results are essentially based on Theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.

How to cite

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Jerbi, Hamadi, Kharrat, Thouraya, and Sioud, Khaled. "Stabilization of homogeneous polynomial systems in the plane." Kybernetika 52.1 (2016): 131-152. <http://eudml.org/doc/276817>.

@article{Jerbi2016,
abstract = {In this paper, we study the problem of stabilization via homogeneous feedback of single-input homogeneous polynomial systems in the plane. We give a complete classification of systems for which there exists a homogeneous stabilizing feedback that is smooth on $\mathbb \{R\}^2 \setminus \lbrace (0,0)\rbrace $ and preserve the homogeneity of the closed loop system. Our results are essentially based on Theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.},
author = {Jerbi, Hamadi, Kharrat, Thouraya, Sioud, Khaled},
journal = {Kybernetika},
keywords = {polynomial system; control system; homogeneous feedback; stabilization},
language = {eng},
number = {1},
pages = {131-152},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stabilization of homogeneous polynomial systems in the plane},
url = {http://eudml.org/doc/276817},
volume = {52},
year = {2016},
}

TY - JOUR
AU - Jerbi, Hamadi
AU - Kharrat, Thouraya
AU - Sioud, Khaled
TI - Stabilization of homogeneous polynomial systems in the plane
JO - Kybernetika
PY - 2016
PB - Institute of Information Theory and Automation AS CR
VL - 52
IS - 1
SP - 131
EP - 152
AB - In this paper, we study the problem of stabilization via homogeneous feedback of single-input homogeneous polynomial systems in the plane. We give a complete classification of systems for which there exists a homogeneous stabilizing feedback that is smooth on $\mathbb {R}^2 \setminus \lbrace (0,0)\rbrace $ and preserve the homogeneity of the closed loop system. Our results are essentially based on Theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.
LA - eng
KW - polynomial system; control system; homogeneous feedback; stabilization
UR - http://eudml.org/doc/276817
ER -

References

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  9. Massera, J. L., 10.2307/1969955, Ann. Math. 64 (1956), 182-206. MR0079179DOI10.2307/1969955
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