On the Lyapunov's Indirect Method for Scalar Differential-Difference Equations

Abstract In this note a constructive proof of the well known Poincare-Lyapunov theorem for scalar differential-difference equations is given. The proof is based in a recent result on complete type Lyapunov-Krasovskii functionals to the robust stability analysis of time-delay systems. The proof is constructive and allow us to obtain an initial estimate of the region of attraction.