  In this paper, we study the stabilization problem of quantum spin-1/2 systems
under continuous-time measurements. In the case without feedback, we show
exponential stabilization around the excited and ground state by providing a
lower bound of the convergence rate. Based on stochastic Lyapunov techniques,
we propose a parametrized measurement-based feedback which ensures exponential
convergence toward the excited state. Moreover, we give a lower bound of the
convergence rate for this case. Then, we discuss the effect of each parameter
appeared in the control law in the convergence rate. Finally, we illustrate the
efficiency of such feedback law through simulations.
