  In this paper we investigate parametrization-free solutions of the problem of
quantum pure state preparation and subspace stabilization by means of
Hamiltonian control, continuous measurement and quantum feedback, in the
presence of a Markovian environment. In particular, we show that whenever
suitable dissipative effects are induced either by the unmonitored environment
or by non Hermitian measurements, there is no need for feedback control to
accomplish the task. Constructive necessary and sufficient conditions on the
form of the open-loop controller can be provided in this case. When open-loop
control is not sufficient, filtering-based feedback control laws steering the
evolution towards a target pure state are provided, which generalize those
available in the literature.
