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math.CA2012
A Converse Sum of Squares Lyapunov Result with a Degree Bound
Matthew M. Peet, Antonis Papachristodoulou
Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we…
math.CA2007
Exponentially Stable Nonlinear Systems have Polynomial Lyapunov Functions on Bounded Regions
Matthew M. Peet
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differe…