Abstract
Homogeneous eigenvalue analysis is a useful tool for analysis of homogeneous systems. We obtained necessary conditions for asymptotic stability in our previous paper. However, any sufficient conditions are not obtained. In this paper, we introduce Euler sphere, and analyze the properties of solutions of homogeneous systems using dilations of Euler sphere. Moreover, we show the equivalence between a trajectory of a projection of a solution and a trajectory of a solution of a projection system. Then, we prove sufficient conditions for asymptotic stability of homogeneous systems. Finally, we demonstrate the effectiveness of the proposed method for a system which has an uncontrollable linear approximation
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