A differential lyapunov framework for contraction analysis
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Peer-reviewed
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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.
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Keywords
Contraction, incremental stability, linearization, Lyapunov methods, nonlinear systems
Journal Title
IEEE Transactions on Automatic Control
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Journal ISSN
0018-9286
1558-2523
1558-2523
Volume Title
59
Publisher
Institute of Electrical and Electronics Engineers (IEEE)