Title :
Feedback stabilization of quantum ensembles: a global convergence analysis on complex flag manifolds
Author :
Altafini, Claudio
Author_Institution :
SISSA-ISAS, Int. Sch. for Adv. Studies, Trieste
Abstract :
In a closed 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 adjoint orbit of the eigenvalues of the density 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
Keywords :
Lyapunov methods; closed loop systems; control system synthesis; convergence; discrete time systems; eigenvalues and eigenfunctions; feedback; quantum theory; stability; time-varying systems; topology; Lyapunov-based time-varying feedback design; closed-loop system; complex flag manifolds; eigenvalues; global convergence analysis; global stabilizability; mixed density operators; periodic orbits; quantum ensembles; quantum mechanical system; unitary feedback stabilization; Algebra; Control systems; Convergence; Density measurement; Eigenvalues and eigenfunctions; Extraterrestrial measurements; Feedback; Open loop systems; Orbits; Quantum mechanics;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.377774