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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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https://hal.inria.fr/hal-01068325
Contributor : Estelle Bouzat <>
Submitted on : Thursday, September 25, 2014 - 2:25:08 PM
Last modification on : Friday, July 26, 2019 - 1:44:05 PM
Long-term archiving on: : Friday, December 26, 2014 - 10:50:39 AM

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  • HAL Id : hal-01068325, version 1

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

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