Controllability of control systems on complex simple lie groups and the topology of flag manifolds

Author(s)

dos Santos, Ariane L. ^[1] ; San Martin, Luiz A. B. ^[2]

Affiliation

^[1] FACIP UFU, Dept Matemat, BR-38304402 Ituiutaba, MG - Brazil

^[2] IMECC UNICAMP, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. 19, n. 2, p. 157-171, APR 2013.
• Web of Science Citations: 4

Abstract

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(alpha) a parts per thousand Sl (2, ) generated by the exp , where is the root space of the root alpha. 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(alpha) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants