  Lyapunov's second theorem is an essential tool for stability analysis of
differential equations. The paper provides an analog theorem for incremental
stability analysis by lifting the Lyapunov function to the tangent bundle. The
Lyapunov function endows the state-space with a Finsler structure. Incremental
stability is inferred from infinitesimal contraction of the Finsler metrics
through integration along solutions curves.
