A Differential Lyapunov Framework for Contraction Analysis

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.

Keywords

4007 Control Engineering, Mechatronics and Robotics, 40 Engineering

Journal Title

IEEE Transactions on Automatic Control

Journal ISSN

0018-9286
1558-2523

Volume Title

59

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Publisher DOI

https://doi.org/10.1109/tac.2013.2285771

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Scholarly Works - Engineering