English

A differential Lyapunov framework for contraction analysis

Systems and Control 2013-10-02 v4 Differential Geometry Dynamical Systems

Abstract

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.

Cite

@article{arxiv.1208.2943,
  title  = {A differential Lyapunov framework for contraction analysis},
  author = {Fulvio Forni and Rodolphe Sepulchre},
  journal= {arXiv preprint arXiv:1208.2943},
  year   = {2013}
}

Comments

15 pages, 1 figure

R2 v1 2026-06-21T21:50:37.140Z