  This paper generalizes the results in [30] concerning feedback stabilization
of target states for N-level quantum angular momentum systems undergoing
quantum non-demolition measurements (QND) in absence of the knowledge about
initial states and parameters. Here we consider multiple measurement operators
and study the stabilization toward a chosen target subspace which is a common
eigenspace of measurement operators. Under the QND conditions, we show that
this analysis provides necessary tools to ensure feedback stabilization based
on a simplified filter whose state is a N-dimensional vector. A numerical
analysis has been proposed in [18]. This paper provides a complete proof for
the use of a simplified filter in feedback stabilization. This has important
practical use as the dimension of quantum systems is usually high. This paper
opens the way toward a complete proof concerning the robustness of a
stabilizing feedback with respect to approximate filters, which is lacking.

Quantum Physics;Optimization and Control;Probability