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In an N-level quantum mechanical system, the problem of unitary feedback stabilization of mixed density operators to periodic orbits admits a natural Lyapunov-based time-varying feedback design. A global description of the domain of attraction of the closed-loop system can be provided based on a "root-space"-like structure of the space of density operators. This convex set foliates as a complex flag manifold where each leaf is identified with the coadjoint orbit of the eigenvalues of thedoi:10.1109/tac.2007.908306 fatcat:rohhougc3ndkharywhesi2grzu