Maxwell Fitzsimmons

A Globally Asymptotically Stable Planar Homogeneous Polynomial Vector Field With No Polynomial Lyapunov Function

Jun Liu, Maxwell Fitzsimmons

We disprove the conjecture that every globally asymptotically stable homogeneous polynomial vector field admits a homogeneous polynomial Lyapunov function. The counterexample is a planar homogeneous cubic polynomial vector field with integer coefficients. It admits no positive de…Read more