  Feedback control of quantum mechanical systems must take into account the
probabilistic nature of quantum measurement. We formulate quantum feedback
control as a problem of stochastic nonlinear control by considering separately
a quantum filtering problem and a state feedback control problem for the
filter. We explore the use of stochastic Lyapunov techniques for the design of
feedback controllers for quantum spin systems and demonstrate the possibility
of stabilizing one outcome of a quantum measurement with unit probability.
