A differential Lyapunov framework for contraction analysis

Forni, Fulvio; Sepulchre, Rodolphe

doi:10.1109/TAC.2013.2285771

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A differential Lyapunov framework for contraction analysis

Forni, Fulvio; Sepulchre, Rodolphe

2014 • In IEEE Transactions on Automatic Control, 59 (3), p. 614-628

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/165111

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10.1109/TAC.2013.2285771

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Keywords :

Contraction; Stability of nonlinear systems; Differential Geometry

Abstract :

[en] 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.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Forni, Fulvio ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

A differential Lyapunov framework for contraction analysis

Publication date :

March 2014

Journal title :

IEEE Transactions on Automatic Control

ISSN :

0018-9286

Publisher :

IEEE, Piscataway, United States - New Jersey

Volume :

Issue :

Pages :

614-628

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 03 April 2014

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226

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203

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167

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