2 papers
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…
math.DS2007
Positive Forms and Stability of Linear Time-Delay Systems
Matthew M. Peet, Antonis Papachristodoulou, Sanjay Lall
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existe…