A Differential Lyapunov Framework for Contraction Analysis
By Fulvio Forni, Rodolphe Sepulchre. IEEE Transactions on Automatic Control, 2012
355 citations recorded by the source corpus.
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.
Subfields: Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/18a5336c7c68a7e8777dc7faac75e3e5ead645a9
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In Control and Systems Engineering
- Sigurdur Freyr Hafstein
- Peter Giesl
- Florian Dörfler
- Francesco Bullo
- Zahra Aminzarey
- Eduardo D. Sontagy
- Xiaohua Ge
- Qing-Long Han
Citations in the corpus
- Synchronization in complex networks of phase oscillators: A survey (2014, methodology): “(24) The application of contraction analysis to the coupled oscillator model (1) yields the incremental exponential stability (24) in 2 -type metrics (Chung and Slotine, 2010, Theorem 7) or in ∞ -type metrics (Forni and Sepulchre, 2014, Example 6).”
- Review on computational methods for Lyapunov functions (2015, methodology): “This implies contraction only with respect to the horizontal component, for details see Forni and Sepulchre 2014 [78].”
- Contraction methods for nonlinear systems: A brief introduction and some open problems (2014, result): “This more general view has been the subject of much recent research, see for example [20], [21], as well as the recent papers [22], [23].”