Retraction obstruction to time-varying stabilization

Emmanuel Bernuau (1) , Wilfrid Perruquetti (1, 2, 3) , Emmanuel Moulay (4)

1 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
2 NON-A - Non-Asymptotic estimation for online systems
3 Centrale Lille
4 XLIM-SIC - SIC

This paper address the problem of the global stabilization on a total space of a fiber bundle with a compact base space. We prove that, under mild assumptions (existence of a continuous section and forward unicity of solutions), no equilibrium of a continuous system defined on such a state space can be globally asymptotically uniformly stabilized using continuous time-varying feedback.

Mots clés: Retraction obstruction; Lyapunov stability; stabilization

Domaines: Automatique / Robotique

Emmanuel Bernuau, Wilfrid Perruquetti, Emmanuel Moulay. Retraction obstruction to time-varying stabilization. Automatica, 2013, 49 (6), pp.1941-1943. ⟨10.1016/j.automatica.2013.03.012⟩. ⟨hal-00862934⟩