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

Emmanuel Bernuau (1, 2) , Denis Efimov (3) , Wilfrid Perruquetti (3, 4)

1 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
2 Dipartimento di Ingegneria dell'Informazione [Pisa]
3 NON-A - Non-Asymptotic estimation for online systems
4 Centrale Lille

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.

Domaines: Automatique / Robotique

Emmanuel Bernuau, Denis Efimov, Wilfrid Perruquetti. On the robustness of homogeneous systems and a homogeneous small gain theorem. IEEE MSC 2014, Oct 2014, Nice/Antibes, France. ⟨hal-01082174⟩