Asymptotic stability implies the existence of a local polynomial Lyapunov function

Details Asymptotic stability implies the existence of a local polynomial Lyapunov function Asymptotic stability implies the existence of a local polynomial Lyapunov function

2012-01-16

arxiv.org/abs/1201.3311v3

Mathematics

Optimization and Control

There is a known counter-example. See "A Globally Asymptotically Stable Polynomial Vector Field with no Polynomial Lyapunov Fu

Scientific paper

We show that every globally asymptotically stable system with a twice
continuously differentiable vector field admits a local polynomial Lyapunov
function on an arbitrary bounded neighborhood of the origin.

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