A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function
arXiv:1803.0608721 citationsh-index: 25
AI Analysis
It provides a counterexample to the common assumption that global asymptotic stability implies existence of a local analytic Lyapunov function, relevant to dynamical systems theory.
The paper presents an explicit 2D polynomial vector field of degree seven with rational coefficients that is globally asymptotically stable but lacks any analytic Lyapunov function, even locally.
We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.