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by F. H. Clarke, Yu. S. Ledyaev, E. D. Sontag, A. I. Subbotin
IEEE Trans. Autom. Control
http://www.math.rutgers.edu/~sontag/FTP_DIR/nonsmooth-feedback.ps.gz
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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 neighborgoods of a desired equilibrium. A major technical problem, and one of contributions of the present paper, concerns the precise meaning of "solution " when using a discontinuous controller. I.
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