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Stabilization of homogeneous polynomial systems in the plane. (English) Zbl 1374.93301
Summary: 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 a theorem of Hahn in which the author gives necessary and sufficient conditions of stability of homogeneous systems in the plane.
MSC:
93D15 Stabilization of systems by feedback
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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