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.
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This research was partially supported by CAPES, Grant No. 3578/82-4.
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Martin, L.S. Invariant control sets on flag manifolds. Math. Control Signal Systems 6, 41–61 (1993). https://doi.org/10.1007/BF01213469
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DOI: https://doi.org/10.1007/BF01213469