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Higher order derivatives of Liapunov functions

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1 Author(s)
Butz, A. ; Northwestern University, Evanston, IL, USA

The problem considered is that of inferring asymptotic stability by examining higher order derivatives of a Liapunov function when examination of only the first derivative does not permit such an inference. It is shown that a seemingly plausible approach using only \dot{V} and \ddot{V} is vacuous. It is also shown that it is possible to infer asymptotic stability by examining \dot{V} and \ddot{V} , and perhaps \ddot{V} .

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Automatic Control, IEEE Transactions on  (Volume:14 ,  Issue: 1 )