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Non-Robustness of Continuous Homogeneous Stabilizers for Affine Control Systems

Abstract : This paper focuses on asymptotic point-stabilization of smooth affine control systems. For asymptotic feedback stabilizers, a simple definition of {robustness} with respect to unmodeled dynamics is adopted. Two theorems are then proved which state sufficient conditions for the {non-robustness} of homogeneous stabilizers. The first theorem, which applies to systems that may contain a drift term, involves a specific class of feedback stabilizers. The second one, which applies to driftless systems and is stated independently of any particular stabilizer, provides a condition related to an eventual loss of rank of the accessibility distribution. One of the consequences of the second result is that, for {chained-form systems}, no (static) continuous homogeneous exponential stabilizer (some of which have been proposed in the literature) can be robust in the sense defined herein. Examples are provided which illustrate a typical application of each result.
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https://hal.inria.fr/inria-00073176
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 12:04:01 PM
Last modification on : Saturday, January 27, 2018 - 1:31:29 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:37:08 PM

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  • HAL Id : inria-00073176, version 1

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David A. Lizárraga, Pascal Morin, Claude Samson. Non-Robustness of Continuous Homogeneous Stabilizers for Affine Control Systems. RR-3508, INRIA. 1998. ⟨inria-00073176⟩

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