The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
On the construction of Lyapunov functions using the sum of squares decomposition
Abstract
A relaxation of Lyapunov's direct method has been proposed elsewhere that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In the paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certain non-polynomial nonlinearities in the vector field to be handled exactly and the constructed Lyapunov functions to contain non-polynomial terms. It also allows robustness analysis to be performed. Some examples are given to illustrate how this is done.
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Cites
Linear Matrix Inequalities in System and Control Theory
Boyd, S., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611970777 · Cited by 21,687
Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
Sturm, J. F. (1999) · Optimization Methods and Software · doi:10.1080/10556789908805766 · Cited by 7,377
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Mathematical Biology: II: Spatial Models and Biomedical Applications
(2003) · Interdisciplinary Applied Mathematics · doi:10.1007/b98869 · Cited by 2,293
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
Parrilo, P. A. (2000) · doi:10.7907/2k6y-ch43 · Cited by 1,802
System analysis via integral quadratic constraints
Megretski, A., & Rantzer, A. (1997) · IEEE Transactions on Automatic Control · doi:10.1109/9.587335 · Cited by 1,521
Introducing SOSTOOLS: a general purpose sum of squares programming solver
Prajna, S., Papachristodoulou, A., & Parrilo, P. A. (2003) · Proceedings of the 41st IEEE Conference on Decision and Control, 2002. · doi:10.1109/cdc.2002.1184594 · Cited by 545
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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
Learning dynamic polynomial proofs
Fawzi, A., Malinowski, M., Fawzi, H., & Fawzi, O. (2019) · arXiv · doi:10.48550/arxiv.1906.01681 · Cited by 8
Metadata
- Authors
- Papachristodoulou, A., & Prajna, S.
- Venue
- Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
- Publisher
- IEEE
- Published
- 2003-08-27
- Volume
- 3
- Pages
- 3482-3487
- ISSN
- 0191-2216 (ISSN-L)
- OpenAlex
- W1496537269
- Cited by
- 461
- References
- 7
- FWCI
- 32.58
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Papachristodoulou, A., & Prajna, S. (2003). On the construction of Lyapunov functions using the sum of squares decomposition. Proceedings of the 41st IEEE Conference on Decision and Control, 2002. https://doi.org/10.1109/cdc.2002.1184414
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