Geodesic
Stabilization of homogeneous polynomial systems in the plane
Kybernetika, Tome 52 (2016) no. 1, pp. 131-152.

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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 $\mathbb{R}^2 \setminus\{ (0,0)\}$ 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.
DOI : 10.14736/kyb-2016-1-0131
Classification : 93D15
Keywords: polynomial system; control system; homogeneous feedback; stabilization 
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Jerbi, Hamadi; Kharrat, Thouraya; Sioud, Khaled. Stabilization of homogeneous polynomial systems in the plane. Kybernetika, Tome 52 (2016) no. 1, pp. 131-152. doi : 10.14736/kyb-2016-1-0131. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2016-1-0131/

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