Further results on Lyapunov functions for slowly time-varying systems
Mathematics of Control, Signals, and Systems, ISSN: 0932-4194, Vol: 19, Issue: 1, Page: 1-21
2007
- 15Citations
- 94Usage
- 2Captures
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Metrics Details
- Citations15
- Citation Indexes15
- 15
- CrossRef11
- Usage94
- Downloads94
- Captures2
- Readers2
Article Description
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model. © Springer-Verlag London Limited 2006.
Bibliographic Details
https://digitalcommons.lsu.edu/mathematics_pubs/1003; https://repository.lsu.edu/mathematics_pubs/1003
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=33846653524&origin=inward; http://dx.doi.org/10.1007/s00498-006-0010-4; http://link.springer.com/10.1007/s00498-006-0010-4; http://link.springer.com/content/pdf/10.1007/s00498-006-0010-4; http://link.springer.com/content/pdf/10.1007/s00498-006-0010-4.pdf; http://link.springer.com/article/10.1007/s00498-006-0010-4/fulltext.html; https://digitalcommons.lsu.edu/mathematics_pubs/1003; https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=2002&context=mathematics_pubs; https://repository.lsu.edu/mathematics_pubs/1003; https://repository.lsu.edu/cgi/viewcontent.cgi?article=2002&context=mathematics_pubs; https://dx.doi.org/10.1007/s00498-006-0010-4; https://link.springer.com/article/10.1007/s00498-006-0010-4; http://www.springerlink.com/index/10.1007/s00498-006-0010-4; http://www.springerlink.com/index/pdf/10.1007/s00498-006-0010-4
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