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Homogeneous Resonance & Asymptotic Stability for Homogeneous Systems

Abstract

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.
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Dates and versions

hal-01068325 , version 1 (25-09-2014)

Identifiers

  • HAL Id : hal-01068325 , version 1

Cite

Henry Hermes, Matthias Kawski, Fabio Ancona. Homogeneous Resonance & Asymptotic Stability for Homogeneous Systems. 2014. ⟨hal-01068325⟩
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