polynomial and sum of squares lyapunov functions

On the Difficulty of Deciding Asymptotic Stability of Cubic Homogeneous Vector Fields

  • Amir Ali Ahmadi
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , ,

    It is well-known that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next interesting degree to consider is equal to three. In this … Read more