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Characterizations of global transversal exponential stability (long version)

Abstract : We study the relationship between the global exponential stability of an invariant manifold and the existence of a positive semi-definite Riemannian metric which is contracted by the flow. In particular, we investigate how the following properties are related to each other (in the global case): i). A manifold is globally "transversally" exponentially stable; ii). The corresponding variational system (c.f. (7) in Section II) admits the same property; iii). There exists a degenerate Riemannian metric which is contracted by the flow and can be used to construct a Lyapunov function. We show that the transverse contraction rate being larger than the expansion of the shadow on the manifold is a sufficient condition for the existence of such a Lyapunov function. An illustration of these tools is given in the context of global full-order observer design.
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https://hal.archives-ouvertes.fr/hal-02851212
Contributor : Vincent Andrieu <>
Submitted on : Thursday, June 11, 2020 - 9:16:41 AM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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  • HAL Id : hal-02851212, version 2

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Vincent Andrieu, Bayu Jayawardhana, Laurent Praly. Characterizations of global transversal exponential stability (long version). 2020. ⟨hal-02851212v2⟩

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