INVARIANT CONTROL SETS ON FLAG MANIFOLDS

Let G be a semisimple Lie group and let S subset-of G be a subsemigrou p with nonempty interior. In this paper we study invariant control set s for the action of S on homogeneous spaces of G. These sets on the bo undary manifolds of the group are characterized in terms of the semisi mple elements contained in int S. From this characterization a result on controllability of control systems on semisimple Lie groups is deri ved. Invariant control sets for the action of S on the boundaries of l arger groups GBAR with G subset-of GBAR are also studied. This latter case includes the action of S on the projective space and on the flag manifolds.