Homogeneous Lyapunov function for homogeneous continuous vector field |
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Authors: | Lionel Rosier |
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Affiliation: | Laboratoire d'Analyse Numérique, Université Paris-Sud, Orsay, France |
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Abstract: | The goal of this article is to provide a construction of a homogeneous Lyapunov function
associated with a system of differential equations
, under the hypotheses: (1)
vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable. Moreover, the Lyapunov function
tends to infinity with x , and belongs to
, with
as large as wanted. As application to the theory of homogeneous systems, we present two well known results of robustness, in a slightly extended form, and with simpler proofs. |
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Keywords: | Local asymptotic stability Lyapunov function homogeneity non-differentiable feedback |
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