Mathematics > Optimization and Control
[Submitted on 16 Mar 2018 (v1), last revised 16 Aug 2018 (this version, v4)]
Title:A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function
View PDFAbstract:We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.
Submission history
From: Bachir El Khadir [view email][v1] Fri, 16 Mar 2018 06:16:48 UTC (179 KB)
[v2] Fri, 22 Jun 2018 23:38:08 UTC (196 KB)
[v3] Sat, 11 Aug 2018 19:20:48 UTC (197 KB)
[v4] Thu, 16 Aug 2018 05:02:40 UTC (206 KB)
Current browse context:
math.OC
References & Citations
Bookmark
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.