Controllability of control systems on complex simple lie groups and the topology of flag manifolds
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Data
2013
Autores
Santos, Ariane Luzia dos [UNESP]
Martin, Luiz Antonio Barreira San
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Resumo
Let S be a subsemigroup with nonempty interior of a connected complex simple Lie group G. It is proved that S = G if S contains a subgroup G (α) ≈ Sl (2, C) generated by the exp g±α, where gα is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of S is contractible in some flag manifold if S is proper, and exploits the fact that several orbits of G (α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements.
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Controllability, Simple Lie groups, Flag manifolds
Como citar
Journal of Dynamical and Control Systems, v. 19, n. 2, p. 157-171, 2013.