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Feedback stabilization of isospectral control systems on complex flag manifolds: application to quantum
 

Summary: 1
Feedback stabilization of isospectral control systems
on complex flag manifolds: application to quantum
ensembles
Claudio Altafini
SISSA-ISAS, Int. School for Advanced Studies
via Beirut 4, 34014 Trieste, Italy
altafini@sissa.it
Abstract-- The convex set of density operators of an
N-level quantum mechanical system foliates as a complex
flag manifold, where each leaf is identified with the adjoint
unitary orbit of the eigenvalues of a density matrix. For
an isospectral bilinear control system evolving on such
an orbit, the state feedback stabilization problem 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 cone of density operators. The
converging conditions are time-independent but depend
on the topology of the flag manifold: it is shown that the

  

Source: Altafini, Claudio - Functional Analysis Sector, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

 

Collections: Engineering; Mathematics