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Homogeneity in the bi-limit as a tool for observer and feedback design

Authors: Vincent Andrieu, Laurent Praly, Alessandro Astolfi, 48th  IEEE  Conference  on  Decision  and  Control, pp. 1050-1055, December 2009, Shanghai, China DOI: 10.1109/CDC.2009.5400263
We introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system.
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BibTeX:
@Proceedings{,
author = {Vincent Andrieu, Laurent Praly, Alessandro Astolfi},
editor = {},
title = {Homogeneity in the bi-limit as a tool for observer and feedback design},
booktitle = {48th  IEEE  Conference  on  Decision  and  Control},
volume = {},
publisher = {},
address = {Shanghai},
pages = {1050-1055},
year = {2009},
abstract = {We introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system.},
keywords = {}}