Recent theoretical and experimental advancements have shown the importance of estimation and control theory to study quantum dynamics even thought this gives rise to unusual models that have not been completely explored yet. The new theoretical and experimental results can lead to the development of new quantum technologies, e.g. quantum computer, cryptography, and quantum memory. In quantum control, we can apply different strategies to design a feedback. Measurement-based feedback and coherent feedback are the most common strategies. In this talk, we consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. By assuming the quantum non-demolition (QND) measurements in open-loop, we construct a strict control Lyapunov function which is based on the open-loop stationary states. We propose a measurement- based feedback scheme which ensures the almost sure convergence towards a target state. Moreover, I discuss the estimation and filtering problem for continuous-time quantum systems which are described by continuous-time stochastic master equations.