||To realize quantum information technology, control for generating a target quantum state is highly necessary. However, in a realistic setup, a quantum state collapses to a mixed state due to dissipation, and it is impossible to generate an arbitrary quantum state generation. Therefore “the reachability analysis”, which quantifies how close the controlled system can approach to a target, is important. In this paper, we develop a general theory giving a fundamental limit on the reachability of quantum state driven by any type of control under dissipation. As an example, we give a theoretical bound on a single-spin system, double-spin system and photon number state with feedback control based on continuous measurement. Moreover, it is shown that the proposed bound can be used as a criterion of easiness of quantum state generation.