Assuming controlled systems are of ideal conditions, this paper studies the application of the Lyapunov method with auxiliary free degrees to mixed-state quantum systems. Based on the LaSalle’s invariant principle, we deduce the largest invariant set of the systems with the control fields and the convergent state set of the system trajectory starting from any initial state, and give the construction principles of free degrees that ensure the system can be asymptotically stabilized to any goal state in the largest invariant set. In order to clearly illustrate the construction principles of free degrees, we do a numerical simulation experiment on a two-level system. At the same time, simulation results show the rationality of the theoretical results obtained in the paper.