A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function

Published: 2018/03/16, Updated: 2018/08/16

Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization algorithms for testing asymptotic stability, nonlinear dynamics, polynomial lyapunov functions, polynomial vector fields, sum of squares optimization Short URL: https://optimization-online.org/?p=15097

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.

A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function

Citation

Article