@inproceedings{e16153b063bb497c937b3558555cce19,
title = "On the algebraization of asymptotic stability analysis for differential systems",
abstract = "In this paper, we analyze the asymptotic stability of autonomous and non-autonomous differential systems by verifying the existence of Lyapunov functions. We start with an algebraic approach for verifying the existence of a Lyapunov function in quadratic form for autonomous systems by first formulating a semi-algebraic system and then solving such a semi-algebraic system by a semi-algebraic system solver. Then, this algebraic approach is extended to parametric autonomous systems and (parametric) non-autonomous systems by introducing quantifiers during algebraization. Experiments on some examples in the literature show the success of our approach in practice.",
keywords = "Asymptotic stability, Lyapunov functions, Quantifier elimination, Semi-algebraic systems",
author = "Zhikun She and Ranran Yan and Bai Xue and Zhiming Zheng",
year = "2009",
language = "英语",
isbn = "9780889867949",
series = "Proceedings of the 11th IASTED International Conference on Control and Applications, CA 2009",
pages = "75--81",
booktitle = "Proceedings of the 11th IASTED International Conference on Control and Applications, CA 2009",
note = "11th IASTED International Conference on Control and Applications, CA 2009 ; Conference date: 13-07-2009 Through 15-07-2009",
}