Transverse exponential stability and applications

Abstract : 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 field of positive definite quadratic forms whose restrictions to the directions transversal to the manifold are decreasing along the flow. We illustrate their relevance with the study of exponential incremental stability. Finally, we apply these results to two control design problems, nonlinear observer design and synchronization. In particular, we provide necessary and sufficient conditions for the design of nonlinear observer and of nonlinear synchronizer with exponential convergence property.
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IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (11), pp.3396 - 3411. 〈10.1109/TAC.2016.2528050〉
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Dernière modification le : lundi 12 novembre 2018 - 10:56:15
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Vincent Andrieu, Bayu Jayawardhana, Laurent Praly. Transverse exponential stability and applications. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2016, 61 (11), pp.3396 - 3411. 〈10.1109/TAC.2016.2528050〉. 〈hal-01232758〉

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