@inproceedings{2638f922c08542d896f3c52cc67383b3,
title = "Stability region analysis using simulations and sum-of-squares programming",
abstract = "The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant sets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite dimensional polynomial parameterizations for the Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of the Lyapunov function candidates are assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute provably invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on several small examples drawn from the literature.",
author = "Ufuk Topcu and Andrew Packard and Peter Seiler and Timothy Wheeler",
year = "2007",
doi = "10.1109/ACC.2007.4283013",
language = "English (US)",
isbn = "1424409888",
series = "Proceedings of the American Control Conference",
pages = "6009--6014",
booktitle = "Proceedings of the 2007 American Control Conference, ACC",
note = "2007 American Control Conference, ACC ; Conference date: 09-07-2007 Through 13-07-2007",
}