An infinite-time relaxation theorem for differential inclusions. Ingalls, B., Sontag, E., & Wang, Y. Proc. Amer. Math. Soc., 131(2):487–499, 2003. abstract bibtex The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.
@ARTICLE{relaxation-DE-PAMS03,
AUTHOR = {B.P. Ingalls and E.D. Sontag and Y. Wang},
JOURNAL = {Proc. Amer. Math. Soc.},
TITLE = {An infinite-time relaxation theorem for differential
inclusions},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {487--499},
VOLUME = {131},
PDF = {../../FTPDIR/relaxation-di-as-appeared.pdf},
ABSTRACT = { The fundamental relaxation result for Lipschitz
differential inclusions is the Filippov-Wazewski Relaxation Theorem,
which provides approximations of trajectories of a relaxed inclusion
on finite intervals. A complementary result is presented, which
provides approximations on infinite intervals, but does not guarantee
that the approximation and the reference trajectory satisfy the same
initial condition. }
}
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