  No quantum measurement can give full information on the state of a quantum
system; hence any quantum feedback control problem is neccessarily one with
partial observations, and can generally be converted into a completely observed
control problem for an appropriate quantum filter as in classical stochastic
control theory. Here we study the properties of controlled quantum filtering
equations as classical stochastic differential equations. We then develop
methods, using a combination of geometric control and classical probabilistic
techniques, for global feedback stabilization of a class of quantum filters
around a particular eigenstate of the measurement operator.
