Feedback Stabilization of Isospectral Control Systems on Complex Flag Manifolds: Application to Quantum Ensembles

Claudio Altafini
2007 IEEE Transactions on Automatic Control  
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 the
more » ... operator. The converging conditions are time-independent but depend from the topology of the flag manifold: it is shown that the closed loop must have a number of equilibria at least equal to the Euler characteristic of the manifold, thus imposing obstructions of topological nature to global stabilizability.
doi:10.1109/tac.2007.908306 fatcat:rohhougc3ndkharywhesi2grzu