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Asymptotic controllability implies feedback stabilization

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4 Author(s)
Clarke, F.H. ; Lyon I Univ., Villeurbanne, France ; Ledyaev, Y.S. ; Sontag, E.D. ; Subbotin, A.I.

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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Automatic Control, IEEE Transactions on  (Volume:42 ,  Issue: 10 )