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Erratum for the paper "Feedback stabilization of isospectral control systems on complex flag
 

Summary: Erratum for the paper "Feedback stabilization of
isospectral control systems on complex flag
manifolds: application to quantum ensembles",
published in IEEE Transactions on Automatic
Control 52(11):2019-2028, 2007.
Claudio Altafini
SISSA-ISAS, International School for Advanced Studies
via Bonomea 265, 34136 Trieste, Italy
March 25, 2011
In a series of papers,[2, 3], X. Wang and S. G. Schirmer found results
slightly in contraddiction with those of [1]. On the complex flag manifolds
S studied in [1, 2, 3] the "competing" equilibria of the desired target d
(denoted antipodal points in [1]) are in general saddle points rather than
repulsive equilibria as stated incorrectly in [1]. This implies that there exist
stable submanifolds connecting two or more of these antipodal points which
are not attracted to d. The results of [1] are still valid almost always, except
for zero-measure submanifolds for which the conditions of Theorem 3 of [1]
are not sufficient to guarantee convergence.
References
[1] C. Altafini. Feedback stabilization of isospectral control systems on complex flag

  

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

 

Collections: Engineering; Mathematics