Invariant control sets on flag manifolds
Identifieur interne : 001F08 ( Main/Exploration ); précédent : 001F07; suivant : 001F09Invariant control sets on flag manifolds
Auteurs : Luiz San Martin [Brésil]Source :
- Mathematics of Control, Signals and Systems [ 0932-4194 ] ; 1993-03-01.
English descriptors
- KwdEn :
- Teeft :
- Abelian, Algebra, Boundary manifolds, Compact group, Control sets, Control signals systems, Control systems, Controllability, Controllable, Coset, Coset space, Fibration, Finite center, Flag manifolds, Grassmannian, Homogeneous space, Homogeneous spaces, Identity component, Invariant control, Invariant control sets, Isotropy, Iwasawa, Iwasawa decomposition, Langlands, Langlands decomposition, Lecture notes, Linear group, Lyapunov exponents, Matrix, Maximal boundary, Maximal flag manifold, Minimal parabolic, Minimal parabolic subgroup, Noncompact, Nonempty, Other hand, Parabolic, Parabolic subalgebra, Parabolic subgroup, Parabolic subgroups, Positive matrices, Positive orthant, Positive system, Positive weyl chamber, Projective space, Semigroup, Semigroups, Semisimple, Subalgebra, Subgroup, Subsemigroup, Subset, Vector fields, Weyl, Weyl group.
Abstract
Abstract: LetG be a semisimple Lie group and letS ⊂G be a subsemigroup with nonempty interior. In this paper we study invariant control sets for the action ofS on homogeneous spaces ofG. These sets on the boundary manifolds of the group are characterized in terms of the semisimple elements contained in intS. From this characterization a result on controllability of control systems on semisimple Lie groups is derived. Invariant control sets for the action of S on the boundaries of larger groups¯G withG ⊂¯G are also studied. This latter case includes the action ofS on the projective space and on the flag manifolds.
Url:
DOI: 10.1007/BF01213469
Affiliations:
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Control Signal Systems</title><idno type="ISSN">0932-4194</idno><idno type="eISSN">1435-568X</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>London</pubPlace><date type="published" when="1993-03-01">1993-03-01</date><biblScope unit="volume">6</biblScope><biblScope unit="issue">1</biblScope><biblScope unit="page" from="41">41</biblScope><biblScope unit="page" to="61">61</biblScope></imprint><idno type="ISSN">0932-4194</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0932-4194</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Controllability</term><term>Flag manifolds</term><term>Invariant control sets</term><term>Semigroups</term><term>Semisimple Lie groups</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Abelian</term><term>Algebra</term><term>Boundary manifolds</term><term>Compact group</term><term>Control sets</term><term>Control signals systems</term><term>Control systems</term><term>Controllability</term><term>Controllable</term><term>Coset</term><term>Coset space</term><term>Fibration</term><term>Finite center</term><term>Flag manifolds</term><term>Grassmannian</term><term>Homogeneous space</term><term>Homogeneous spaces</term><term>Identity component</term><term>Invariant control</term><term>Invariant control sets</term><term>Isotropy</term><term>Iwasawa</term><term>Iwasawa decomposition</term><term>Langlands</term><term>Langlands decomposition</term><term>Lecture notes</term><term>Linear group</term><term>Lyapunov exponents</term><term>Matrix</term><term>Maximal boundary</term><term>Maximal flag manifold</term><term>Minimal parabolic</term><term>Minimal parabolic subgroup</term><term>Noncompact</term><term>Nonempty</term><term>Other hand</term><term>Parabolic</term><term>Parabolic subalgebra</term><term>Parabolic subgroup</term><term>Parabolic subgroups</term><term>Positive matrices</term><term>Positive orthant</term><term>Positive system</term><term>Positive weyl chamber</term><term>Projective space</term><term>Semigroup</term><term>Semigroups</term><term>Semisimple</term><term>Subalgebra</term><term>Subgroup</term><term>Subsemigroup</term><term>Subset</term><term>Vector fields</term><term>Weyl</term><term>Weyl group</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: LetG be a semisimple Lie group and letS ⊂G be a subsemigroup with nonempty interior. In this paper we study invariant control sets for the action ofS on homogeneous spaces ofG. These sets on the boundary manifolds of the group are characterized in terms of the semisimple elements contained in intS. From this characterization a result on controllability of control systems on semisimple Lie groups is derived. Invariant control sets for the action of S on the boundaries of larger groups¯G withG ⊂¯G are also studied. This latter case includes the action ofS on the projective space and on the flag manifolds.</div></front></TEI><affiliations><list><country><li>Brésil</li></country><region><li>État de São Paulo</li></region><settlement><li>Campinas</li></settlement><orgName><li>Université d'État de Campinas</li></orgName></list><tree><country name="Brésil"><region name="État de São Paulo"><name sortKey="Martin, Luiz San" sort="Martin, Luiz San" uniqKey="Martin L" first="Luiz San" last="Martin">Luiz San Martin</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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