@article{a8b8de94046244859ebc582803b0e166,
title = "A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function",
abstract = "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.",
keywords = "Algorithms for testing asymptotic stability, Nonlinear dynamics, Polynomial Lyapunov functions, Polynomial vector fields, Sum of squares optimization",
author = "Ahmadi, {Amir Ali} and {El Khadir}, Bachir",
note = "Funding Information: We are grateful to the anonymous Associate Editor and the anonymous referees whose constructive feedback has improved our presentation considerably. The authors are with the department of Operations Research and Financial Engineering at Princeton University. This work was partially supported by the DARPA Young Faculty Award, the Young Investigator Award of the AFOSR, the CAREER Award of the NSF, the Google Faculty Award, and the Sloan Fellowship. Funding Information: We are grateful to the anonymous Associate Editor and the anonymous referees whose constructive feedback has improved our presentation considerably. The authors are with the department of Operations Research and Financial Engineering at Princeton University. This work was partially supported by the DARPA Young Faculty Award , the Young Investigator Award of the AFOSR , the CAREER Award of the NSF , the Google Faculty Award , and the Sloan Fellowship . Publisher Copyright: {\textcopyright} 2018",
year = "2018",
month = nov,
doi = "10.1016/j.sysconle.2018.07.013",
language = "English (US)",
volume = "121",
pages = "50--53",
journal = "Systems and Control Letters",
issn = "0167-6911",
publisher = "Elsevier",
}