Controllability of periodic linear systems, the Poincare sphere, and quasi-affine systems

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 Poincaré 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.