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In this technical note, two problems have been investigated. The first one concerns the global asymptotic feedback stabilization of homogeneous systems. For these systems, it is shown that local asymptotic stabilization implies the global dynamic feedback stabilization one. The second problem consists to show that under a weak assumption on the observability, if a state affine system is locally asymptotically stabilizable then it becomes globally asymptotically stabilizable by using a discontinuous output feedback.