  We discuss the multilevel control problem for linear dynamical systems,
consisting in designing a piece-wise constant control function taking values in
a finite-dimensional set. In particular, we provide a complete characterization
of multilevel controls through a duality approach, based on the minimization of
a suitable cost functional. In this manner we build optimal multi-level
controls and characterize the time needed for a given ensemble of levels to
assure the controllability of the system. Moreover, this method leads to
efficient numerical algorithms for computing multilevel controls.
