Abstract
As is well known, the stability of a dynamical system in two dimensions may be demonstrated in a very intuitive fashion from the existence of a suitable positive-definite Liapunov function, providing the contours of this function in a neighborhood of the stable point are Jordan curves. It is shown that the Liapunov function will certainly have this property if the stable point is an isolated stationary point in the sense of the Clarke calculus, but a counterexample is given if this assumption is weakened to the stable point being an isolated local extremum.
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Communicated by T. L. Vincent
This work was carried out with the support of the Natural Sciences and Engineering Council of Canada, which is gratefully acknowledged.
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Chamberland, M., Lewis, A.S. Contours of Liapunov functions. J Optim Theory Appl 80, 149–160 (1994). https://doi.org/10.1007/BF02196598
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DOI: https://doi.org/10.1007/BF02196598