Abstract
This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further.
| Original language | English |
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| Title of host publication | Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control |
| Publisher | IEEE |
| Publication date | 23. Jan 2018 |
| Pages | 4884-4889 |
| ISBN (Print) | 978-1-5090-2874-0 |
| ISBN (Electronic) | 978-1-5090-2873-3, 978-1-5090-2872-6 |
| DOIs | |
| Publication status | Published - 23. Jan 2018 |
| Externally published | Yes |
| Event | 56th IEEE Annual Conference on Decision and Control - Melbourne, Australia Duration: 12. Dec 2017 → 15. Dec 2017 Conference number: 56 |
Conference
| Conference | 56th IEEE Annual Conference on Decision and Control |
|---|---|
| Number | 56 |
| Country/Territory | Australia |
| City | Melbourne |
| Period | 12/12/2017 → 15/12/2017 |
| Sponsor | ANCA Motion, City of Melbourne, University of Melbourne, University of Newcastle , United Technologies Research Center (UTRC) |