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On transverse exponential stability and its use in incremental stability, observer and synchronization

Abstract : We study the relation between the exponential stability of an invariant manifold and the existence of a Riemannian metric for which the flow is "transversally" contracting. More precisely, we investigate how the following properties are related to each other: i). A manifold is "transversally" exponentially stable; ii). The "transverse" linearization along any solution in the manifold is exponentially stable; iii). There exists a Riemannian metric for which the flow is "transversally" contracting. We show the relevance of these results in the study of incremental stability, observer design and synchronization.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00971475
Contributor : François Chaplais <>
Submitted on : Wednesday, April 2, 2014 - 10:28:39 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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Vincent Andrieu, Bayu Jayawardhana, Laurent Praly. On transverse exponential stability and its use in incremental stability, observer and synchronization. Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, Dec 2013, Firenze, Italy. pp.5915 - 5920, ⟨10.1109/CDC.2013.6760822⟩. ⟨hal-00971475⟩

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