Asymptotic Stability and Smooth Lyapunov Functions

@article{Clarke1998AsymptoticSA,
  title={Asymptotic Stability and Smooth Lyapunov Functions},
  author={Frank H. Clarke and Yu. S. Ledyaev and Ronald J. Stern},
  journal={Journal of Differential Equations},
  year={1998},
  volume={149},
  pages={69-114}
}
Abstract We establish that differential inclusions corresponding to upper semicontinuous multifunctions are strongly asymptotically stable if and only if there exists a smooth Lyapunov function. Since well-known concepts of generalized solutions of differential equations with discontinuous right-hand side can be described in terms of solutions of certain related differential inclusions involving upper semicontinuous multifunctions, this result gives a Lyapunov characterization of asymptotic… 

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TLDR
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Results on converse Lyapunov functions from class-KL estimates

  • A. TeelL. Praly
  • Mathematics
    Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304)
  • 1999
We state results on converse Lyapunov functions for differential inclusions where a positive semidefinite function of the solutions satisfies a class-KL estimate in terms of time and a second
...

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