The stochastic open quantum system models undergoing continuous measurement in different cases were investigated. For different stochastic open quantum system models affected by the measurement, the model establishment conditions, the composition of model component and its effect were analyzed. For the simplified models, the processes of simplification were also analyzed. At the same time, the relationships between different models were compared. Based on the stochastic open quantum systems with the state estimation, the existed switch and continuous control laws which were used to transfer the quantum states between the eigenstates were comparatively analyzed from their control ideas, characteristics, control effect, condition of using, to the improving process. The feedback controller design was also discussed under the influences of environment decoherence and time-delay.