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On the robustness of homogeneous systems and a homogeneous small gain theorem

This paper is devoted to the study of the robustness properties stemming from geometric homogeneity. More precisely, we show that a continuous homogeneous system, which is asymptotically stable without perturbation, is always ISS w.r.t. a perturbation. We characterize the asymptotic gain of such a disturbed system and state a so-called homogeneous small gain theorem based on this estimation.