https://inria.hal.science/hal-01068325Hermes, HenryHenryHermesDepartment of Applied Mathematics [Boulder] - University of Colorado [Boulder]Kawski, MatthiasMatthiasKawskiASU - Arizona State University [Tempe]Ancona, FabioFabioAnconaDipartimento di Matematica Pura e Applicata [Padova] - Unipd - Università degli Studi di Padova = University of PaduaHomogeneous Resonance & Asymptotic Stability for Homogeneous SystemsHAL CCSD2014[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Bouzat, EstelleSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - 2014-09-25 14:25:082022-11-25 19:07:322014-09-25 15:43:15enPreprints, Working Papers, ...application/pdf1This paper surveys existing necessary conditions, and gives new conditions based on homogeneous resonance, for a homogeneous system to admit a homogeneous (of correct order) continuous, asymptotically stabilizing, state, feedback control. Such conditions are basic in utilizing high order, homogeneous, approximations of non-linear systems to construct asymptotically stabilizing feedback controls when linear approximations of the nonlinear system are not locally controllable. For a class of three dimensional, homogeneous, locally controllable, systems, we determine at which resonance values they can be stabilized.