On the Existence of Polynomial Lyapunov Functions for Rationally Stable Vector Fields

Tobias Leth, Rafal Wisniewski, Christoffer Sloth

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

2 Citationer (Scopus)

Resumé

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
OriginalsprogEngelsk
Titel2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Antal sider6
Vol/bind2018-January
ForlagIEEE
Publikationsdato18 jan. 2018
Sider4884-4889
ISBN (Trykt) 978-1-5090-2874-0
ISBN (Elektronisk)978-1-5090-2873-3
DOI
StatusUdgivet - 18 jan. 2018
Begivenhed56th IEEE Conference on Decision and Control (CDC) - Melbourne, Australien
Varighed: 12 dec. 201715 dec. 2017

Konference

Konference56th IEEE Conference on Decision and Control (CDC)
LandAustralien
ByMelbourne
Periode12/12/201715/12/2017

Citer dette

Leth, T., Wisniewski, R., & Sloth, C. (2018). On the Existence of Polynomial Lyapunov Functions for Rationally Stable Vector Fields. I 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (Bind 2018-January, s. 4884-4889). IEEE. https://doi.org/10.1109/CDC.2017.8264381
Leth, Tobias ; Wisniewski, Rafal ; Sloth, Christoffer. / On the Existence of Polynomial Lyapunov Functions for Rationally Stable Vector Fields. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Bind 2018-January IEEE, 2018. s. 4884-4889
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Leth, T, Wisniewski, R & Sloth, C 2018, On the Existence of Polynomial Lyapunov Functions for Rationally Stable Vector Fields. i 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. bind 2018-January, IEEE, s. 4884-4889, 56th IEEE Conference on Decision and Control (CDC) , Melbourne, Australien, 12/12/2017. https://doi.org/10.1109/CDC.2017.8264381

On the Existence of Polynomial Lyapunov Functions for Rationally Stable Vector Fields. / Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer.

2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Bind 2018-January IEEE, 2018. s. 4884-4889.

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

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AB - 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

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Leth T, Wisniewski R, Sloth C. On the Existence of Polynomial Lyapunov Functions for Rationally Stable Vector Fields. I 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Bind 2018-January. IEEE. 2018. s. 4884-4889 https://doi.org/10.1109/CDC.2017.8264381