On the existence of polynomial Lyapunov functions for rationally stable vector fields

Tobias Leth; Rafal Wisniewski; Christoffer Sloth

doi:10.1109/CDC.2017.8264381

On the existence of polynomial Lyapunov functions for rationally stable vector fields

Tobias Leth, Rafal Wisniewski, Christoffer Sloth

Aalborg Universitet

Publikation: Kapitel i bog/rapport/konference-proceeding › Konferencebidrag i proceedings › Forskning › peer review

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.

Originalsprog	Engelsk
Titel	Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control
Forlag	IEEE
Publikationsdato	23. jan. 2018
Sider	4884-4889
ISBN (Trykt)	978-1-5090-2874-0
ISBN (Elektronisk)	978-1-5090-2873-3, 978-1-5090-2872-6
DOI	https://doi.org/10.1109/CDC.2017.8264381
Status	Udgivet - 23. jan. 2018
Udgivet eksternt	Ja
Begivenhed	56th Annual Conference on Decision and Control - Melbourne, Australien Varighed: 12. dec. 2017 → 15. dec. 2017 Konferencens nummer: 56

Konference

Konference	56th Annual Conference on Decision and Control
Nummer	56
Land/Område	Australien
By	Melbourne
Periode	12/12/2017 → 15/12/2017
Sponsor	ANCA Motion, City of Melbourne, University of Melbourne, University of Newcastle , United Technologies Research Center (UTRC)

Dokumenter og links

10.1109/CDC.2017.8264381

Citationsformater

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title = "On the existence of polynomial Lyapunov functions for rationally stable vector fields",

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.",

author = "Tobias Leth and Rafal Wisniewski and Christoffer Sloth",

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AU - Leth, Tobias

AU - Wisniewski, Rafal

AU - Sloth, Christoffer

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PY - 2018/1/23

Y1 - 2018/1/23

N2 - 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.

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.

U2 - 10.1109/CDC.2017.8264381

DO - 10.1109/CDC.2017.8264381

M3 - Article in proceedings

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SN - 978-1-5090-2874-0

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BT - Proceedings of the 2017 IEEE 56th Annual Conference on Decision and Control

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T2 - 56th IEEE Annual Conference on Decision and Control

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ER -

On the existence of polynomial Lyapunov functions for rationally stable vector fields

Abstract

Konference

Dokumenter og links

Fingeraftryk

Citationsformater