Displaying similar documents to “Geometry of control-affine systems.”

Affine Independence in Vector Spaces

Karol Pąk (2010)

Formalized Mathematics

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In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties...

Control affine systems on solvable three-dimensional Lie groups, I

Rory Biggs, Claudiu C. Remsing (2013)

Archivum Mathematicum

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We seek to classify the full-rank left-invariant control affine systems evolving on solvable three-dimensional Lie groups. In this paper we consider only the cases corresponding to the solvable Lie algebras of types II, IV, and V in the Bianchi-Behr classification.

Abstract separation theorems of Rodé type and their applications

Kazimierz Nikodem, Zsolt Páles, Szymon Wąsowicz (1999)

Annales Polonici Mathematici

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Sufficient and necessary conditions are presented under which two given functions can be separated by a function Π-affine in Rodé sense (resp. Π-convex, Π-concave). As special cases several old and new separation theorems are obtained.