Kybernetika 52 no. 1, 131-152, 2016

Stabilization of homogeneous polynomial systems in the plane

Hamadi Jerbi, Thouraya Kharrat and Khaled SioudDOI: 10.14736/kyb-2016-1-0131

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 $\mathbb{R}^2 \setminus\{ (0,0)\}$ 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.

Keywords:

stabilization, polynomial system, control system, homogeneous feedback

Classification:

93D15

paper.pdf

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