Converse results on existence of sum of squares Lyapunov functions

@article{Ahmadi2011ConverseRO,
  title={Converse results on existence of sum of squares Lyapunov functions},
  author={Amir Ali Ahmadi and Pablo A. Parrilo},
  journal={IEEE Conference on Decision and Control and European Control Conference},
  year={2011},
  pages={6516-6521}
}
Despite the pervasiveness of sum of squares (sos) techniques in Lyapunov analysis of dynamical systems, the converse question of whether sos Lyapunov functions exist whenever polynomial Lyapunov functions exist has remained elusive. In this paper, we first show via an explicit counterexample that if the degree of the polynomial Lyapunov function is fixed, then sos programming can fail to find a valid Lyapunov function even though one exists. On the other hand, if the degree is allowed to… CONTINUE READING

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