An implicit Lyapunov-based approach is proposed for generating
trajectories of a finite dimensional controlled quantum system. The
main difficulty comes from the fact that we consider the degenerate
case where the linearized control system around the target state is not
controllable. The controlled Lyapunov function is defined by an
implicit equation and its existence is shown by a fix point theorem.
The convergence analysis is done using LaSalle invariance principle.
Closed-loop simulations illustrate the performance of such feedback
laws for the open-loop control of a test case considered by chemists. Full paper.