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Genericity of observability and the existence of asymptotic observers

J. GauthierI Kupka — 1995

Banach Center Publications

In this paper, we deal with the genericity of the observability property and the existence of asymptotic observers for nonlinear systems. In the case where the number of outputs is larger than the number of inputs and the state space is compact, we prove that observability in a very strong sense (more or less, observability for each sufficiently differentiable input) is generic. This is obtained by using standard (but not easy) transversality arguments. For the inputs that are bounded with their...

Sub-Riemannian sphere in Martinet flat case

A. AgrachevB. BonnardM. ChybaI. Kupka — 2010

ESAIM: Control, Optimisation and Calculus of Variations

This article deals with the local sub-Riemannian geometry on ℜ, () where is the distribution ker being the Martinet one-form : and is a Riemannian metric on . We prove that we can take as a sum of squares . Then we analyze the flat case where 1. We parametrize the set of geodesics using elliptic integrals. This allows to compute the exponential mapping, the wave front, the conjugate and cut loci and the sub-Riemannian sphere. A direct consequence of our computations is to show that...

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