  In this paper, we consider stochastic master equations describing the
evolutions of quantum systems interacting with electromagnetic fields
undergoing continuous-time measurements. In particular, we study feedback
control of quantum spin-1/2 systems in the case of unawareness of initial
states and in presence of measurement imperfections. We prove that the fidelity
between the actual quantum filter and its associated estimated filter converges
to one under appropriate assumption on the feedback controller. This shows the
asymptotic convergence of such filters. In addition, for spin-J systems, we
discuss heuristically the asymptotic behavior of the actual quantum filter and
its associated estimated filter and the possibility of exponentially
stabilizing such systems towards an eigenvector of the measurement operator by
an appropriate feedback.
