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Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2021

Characterizations of Global Transversal Exponential Stability

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Résumé

We study the relationship between the global exponential stability of an invariant manifold and the existence of a semi-definite positive 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. (8) 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.

Dates et versions

hal-03500595 , version 1 (22-12-2021)

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Vincent Andrieu, Bayu Jayawardhana, Laurent Praly. Characterizations of Global Transversal Exponential Stability. IEEE Transactions on Automatic Control, 2021, 66 (8), pp.3682-3694. ⟨10.1109/TAC.2020.3036021⟩. ⟨hal-03500595⟩
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