%0 Unpublished work %T Homogeneous Resonance & Asymptotic Stability for Homogeneous Systems %+ Department of Applied Mathematics [Boulder] %+ Arizona State University [Tempe] (ASU) %+ Dipartimento di Matematica Pura e Applicata [Padova] %A Hermes, Henry %A Kawski, Matthias %A Ancona, Fabio %8 2014-09-25 %D 2014 %Z Mathematics [math]/Optimization and Control [math.OC]Preprints, Working Papers, ... %X This 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. %G English %2 https://inria.hal.science/hal-01068325/document %2 https://inria.hal.science/hal-01068325/file/asfc.pdf %L hal-01068325 %U https://inria.hal.science/hal-01068325 %~ INSMI %~ OPENAIRE %~ SADCO %~ TDS-MACS