Controllability of group translations

We analyze controllability of group translations. Compact groups are shown to be controllable if the input set is of positive measure and contains an ergodic element. A particular example is that of torus translations /spl theta//spl rarr//spl theta/+/spl omega/, where /spl omega/ is chosen from an input set U/spl sub/T which are proven to be controllable if the input set is of non-zero measure. Controllability of R/sup n/ under addition is discussed.