The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Discontinuous dynamical systems
Open accessAbstract
This article has presented an introductory tutorial on discontinuous dynamical systems. Various examples illustrate the pertinence of the continuity and Lipschitzness properties that guarantee the existence and uniqueness of classical solutions to ordinary differential equations. The lack of these properties in examples drawn from various disciplines motivates the need for more general notions than the classical one. First, we introduced notions of solution for discontinuous systems. Second, we reviewed the available tools from non- smooth analysis to study the gradient information of candidate Lyapunov functions. And, third, we presented nonsmooth stability tools to characterize the asymptotic behavior of solutions.
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Citations
Cites
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Cited by
Goebel, R., Sanfelice, R. G., & Teel, A. R. (2009) · IEEE Control Systems · doi:10.1109/mcs.2008.931718 · Cited by 1,656
Nonsmooth Barrier Functions With Applications to Multi-Robot Systems
Glotfelter, P., Cortes, J., & Egerstedt, M. (2017) · IEEE Control Systems Letters · doi:10.1109/lcsys.2017.2710943 · Cited by 312
Continuous-time distributed convex optimization on weight-balanced digraphs
Gharesifard, B., & Cortes, J. (2012) · 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc.2012.6426897 · Cited by 32
Wang, X., & Chen, X. (2026) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2026.3684791
Metadata
- Venue
- IEEE Control Systems
- Published
- 2008-06
- Volume
- 28
- Issue
- 3
- Pages
- 36-73
- ISSN
- 1066-033X (ISSN-L)
- 1941-000X
- OpenAlex
- W2048723778
- Cited by
- 1,068
- References
- 1
- FWCI
- 55.41
- Type
- journal article
- Language
- en
- Open access
- green
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