  For periodic linear control systems with bounded control range, an
autonomized system is introduced by adding the phase to the state of the
system. Here a unique control set (i.e., a maximal set of approximate
controllability) with nonvoid interior exists. It is determined by the spectral
subspaces of the homogeneous part which is a periodic linear differential
equation. Using the Poincar\'e sphere one obtains a compactification of the
state space allowing us to describe the behavior near infinity of the original
control system. Furthermore, an application to quasi-affine systems yields a
unique control set with nonvoid interior.
