Asymptotic Controllability Implies Feedback Stabilization

@inproceedings{ClarkeAsymptoticCI,
  title={Asymptotic Controllability Implies Feedback Stabilization},
  author={Francis H. Clarke and Yu. S. Ledyaev and Eduardo D. Sontag and Andrei Subbotin}
}
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. 
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