Homogeneity of differential inclusions

Abstract : In this chapter the notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontin-uous setting: the equivalence of the global asymptotic stability and the existence of a homogeneous Lyapunov function; the link between finite-time stability and negative degree of homogeneity; the equivalence between attractivity and asymptotic stability are among the proved results.
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Chapitre d'ouvrage
Recent Trends in Sliding Mode Control, 2016
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  • HAL Id : hal-01405148, version 1

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Emmanuel Bernuau, Denis Efimov, Wilfrid Perruquetti, Andrey Polyakov. Homogeneity of differential inclusions. Recent Trends in Sliding Mode Control, 2016. 〈hal-01405148〉

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