The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
A Differential Lyapunov Framework for Contraction Analysis
Open accessAbstract
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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Cites
Isidori, A. (1995) · Communications and Control Engineering · doi:10.1007/978-1-84628-615-5 · Cited by 6,755
Differentiable dynamical systems
Smale, S. (1967) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1967-11798-1 · Cited by 3,027
Smooth stabilization implies coprime factorization
Sontag, E. D. (1989) · IEEE Transactions on Automatic Control · doi:10.1109/9.28018 · Cited by 2,717
Differentiable Dynamical Systems
Smale, S. (1980) · The Mathematics of Time · doi:10.1007/978-1-4613-8101-3_1 · Cited by 2,478
Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
Smith, H. (2008) · Mathematical Surveys and Monographs · doi:10.1090/surv/041 · Cited by 2,294
Distributed asynchronous deterministic and stochastic gradient optimization algorithms
Tsitsiklis, J., Bertsekas, D., & Athans, M. (1986) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1986.1104412 · Cited by 1,967
Optimization Algorithms on Matrix Manifolds
Absil, P.-A., Mahony, R., & Sepulchre, R. (2008) · Princeton University Press eBooks · doi:10.1515/9781400830244 · Cited by 1,840
Self-citationAn Introduction to Differentiable Manifolds and Riemannian Geometry
(1975) · Pure and Applied Mathematics · doi:10.1016/s0079-8169(08)x6065-9 · Cited by 1,778
An Introduction to Riemann-Finsler Geometry
Bao, D., Chern, S.-S., & Shen, Z. (2000) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-1268-3 · Cited by 1,690
Contraction Analysis of Nonlinear SystemsPreprint
Slotine, J.-J. E. (1999) · Cited by 1,530
Cited by
Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview
Tsukamoto, H., Chung, S.-J., & Slotine, J.-J. E. (2021) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2021.10.001 · Cited by 145
Contraction Analysis of Almost Surely Monotone Discrete-Time Systems With Unknown Time Delay
Kawano, Y., & Hosoe, Y. (2025) · IEEE Control Systems Letters · doi:10.1109/lcsys.2025.3574230 · Cited by 1
Metadata
- Authors
- Forni, F., & Sepulchre, R.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2014-03
- Volume
- 59
- Issue
- 3
- Pages
- 614-628
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2036216368
- Cited by
- 332
- References
- 28
- FWCI
- 35.73
- Type
- journal article
- Language
- en
- Open access
- green
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