Controllability of nilpotent systems

Victor Bravo

Displaying similar documents to “Controllability of nilpotent systems”

Nilpotent control systems.

Elisabeth Remm, Michel Goze (2002)

Revista Matemática Complutense

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We study the class of matrix controlled systems associated to graded filiform nilpotent Lie algebras. This generalizes the non- linear system corresponding to the control of the trails pulled by car.

Controllability of right invariant systems on semi-simple Lie groups

R. El Assoudi, J. Gauthier, I. Kupka (1995)

Banach Center Publications

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We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.

On the Moore formula of compact nilmanifolds.

Hamrouni, Hatem (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Some geometrical properties of infinite-dimensional bilinear controlled systems

Naceurdine Bensalem, Fernand Pelletier (1999)

Banach Center Publications

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The study of controlled infinite-dimensional systems gives rise to many papers (see for instance [GXL], [GXB], [X]) but it is also motivated by various mathematical problems: partial differential equations ([BP]), sub-Riemannian geometry on infinite-dimensional manifolds ([Gr]), deformations in loop-spaces ([AP], [PS]). The first difference between finite and infinite-dimensional cases is that solutions in general do not exist (even locally) for every given control function. The aim...

The exponential map and differential equations on real Lie groups.

Moskowitz, Martin, Sacksteder, Richard (2003)

Journal of Lie Theory

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Lie algebras of a class of top spaces.

Molaei, M.R., Farhangdoost, M.R. (2009)

Balkan Journal of Geometry and its Applications (BJGA)

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The classification of all simple Lie groups with surjective exponential map.

Wüstner, Michael (2005)

Journal of Lie Theory

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Some necessary and sufficient conditions for nilpotent $n$ -Lie superalgebras

Baoling Guan, Liangyun Chen, Yao Ma (2014)

Czechoslovak Mathematical Journal

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The paper studies nilpotent $n$ -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for $n$ -Lie superalgebras which is a generalization of those for $n$ -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent $n$ -Lie superalgebras and obtain several sufficient conditions for an $n$ -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal...

Controllability of the Benjamin-Bona-Mahony equation.

Adames, N., Leiva, H., Sánchez, J. (2008)

Divulgaciones Matemáticas

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Forward invariant sets, homogeneity and small-time local controllability

Mikhail Krastanov (1995)

Banach Center Publications

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The property of forward invariance of a subset of $R^{n}$ with respect to a differential inclusion is characterized by using the notion of a perpendicular to a set. The obtained results are applied for investigating the dependence of the small-time local controllability of a homogeneous control system on parameters.

On $k$ -filiform Lie algebras. I.

Campoamor Stursberg, O.R. (2002)

Acta Mathematica Universitatis Comenianae. New Series

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A nilpotent Lie algebra and eigenvalue estimates

Jacek Dziubański, Andrzej Hulanicki, Joe Jenkins (1995)

Colloquium Mathematicae

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The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on $ℝ^{n}$ with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.