stability of differential equations

Stability of Polynomial Differential Equations: Complexity and Converse Lyapunov Questions

  • Amir Ali Ahmadi
  • Pablo A. Parrilo
    • Categories Control Applications, Convex Optimization, Semi-definite Programming Tags , , , ,

    We consider polynomial differential equations and make a number of contributions to the questions of (i) complexity of deciding stability, (ii) existence of polynomial Lyapunov functions, and (iii) existence of sum of squares (sos) Lyapunov functions. (i) We show that deciding local or global asymptotic stability of cubic vector fields is strongly NP-hard. Simple variations … Read more