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