  A Lyapunov-based control design for natural trajectory-tracking problems is
analyzed for quantum states where the analysis in the generic case is not
applicable. Using dynamical systems tools we show almost global asymptotic
stability for stationary target states subject to certain conditions on the
Hamiltonians, and discuss effectiveness of the design when these conditions are
not satisfied. For pseudo-pure target states the effectiveness of the design is
studied further for both stationary and non-stationary states using alternative
tools.
