Feedback Stabilization and Lyapunov Functions

@article{Clarke2000FeedbackSA,
  title={Feedback Stabilization and Lyapunov Functions},
  author={Francis H. Clarke and Yuri S. Ledyaev and L. Rifford and R. J. Stern},
  journal={SIAM J. Control and Optimization},
  year={2000},
  volume={39},
  pages={25-48}
}
Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish a robustness property of the feedback relative to measurement error commensurate with the sampling rate of the control implementation scheme. 
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