Homogeneous continuous finite-time observer for the triple integrator

Abstract : In this paper we consider the continuous homogeneous observer defined in [1] in the case of the triple in-tegrator. In [1], convergence of the algorithm was only proved when the degree of homogeneity was sufficiently close to 0 without more tractable information. We show here that, in the case of the triple integrator, the observer presents global finite-time stability for any negative degree under constructive conditions on the gains. This is achieved with a homogeneous Lyapunov function design. Simulations of the proposed observer are also provided.
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Emmanuel Bernuau, Denis Efimov, Emmanuel Moulay, Wilfrid Perruquetti. Homogeneous continuous finite-time observer for the triple integrator. ECC'15 - 14th annual European Control Conference, Jul 2015, Linz, Austria. ⟨hal-01140339⟩

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