Continuous control-Lyapunov functions for asymptotically controllable time-varying systems. Albertini, F. and Sontag, E. Internat. J. Control, 72(18):1630–1641, 1999. abstract bibtex This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set.
@ARTICLE{MR1733874,
AUTHOR = {F. Albertini and E.D. Sontag},
JOURNAL = {Internat. J. Control},
TITLE = {Continuous control-Lyapunov functions for asymptotically
controllable time-varying systems},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {18},
PAGES = {1630--1641},
VOLUME = {72},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/albertini-clf.pdf},
ABSTRACT = { This paper shows that, for time varying systems, global
asymptotic controllability to a given closed subset of the state
space is equivalent to the existence of a continuous control-Lyapunov
function with respect to the set. }
}