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Book Sections Year : 2016

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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Dates and versions

hal-01405148 , version 1 (29-11-2016)

Identifiers

  • HAL Id : hal-01405148 , version 1

Cite

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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