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Asymptotic controllability implies feedback stabilization
Clarke, F.H.   Ledyaev, Y.S.   Sontag, E.D.   Subbotin, A.I.  
Lyon I Univ., Villeurbanne;

This paper appears in: Automatic Control, IEEE Transactions on
Publication Date: Oct 1997
Volume: 42,  Issue: 10
On page(s): 1394-1407
ISSN: 0018-9286
References Cited: 30
CODEN: IETAA9
INSPEC Accession Number: 5726771
Digital Object Identifier: 10.1109/9.633828
Current Version Published: 2002-08-06

Abstract
It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a control-Lyapunov function, iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium. A major technical problem, and one of the contributions of the present paper, concerns the precise meaning of “solution” when using a discontinuous controller

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