Exact output stabilization at unobservable points: Analysis via an example

In this paper, we analyze, via a simple academic example from quantum control, the problem of dynamic exact output stabilization, when the point where we want to stabilize to corresponds to a control value that makes the system unobservable. The stability analysis is performed in three steps. We have validated the method for a specific case, but the idea can be extended to more general problems. In particular, the method can be applied to the case of Killing systems that are injectable into bilinear skew-symmetric systems.