In the proceedings of the American Control Conference, pp. 6009-6014, 2007 (with A. Packard, P. Seiler, and T. Wheeler).
@INPROCEEDINGS{4283013,
title={Stability Region Analysis Using Simulations and Sum-of-Squares Programming},
author={Topcu, U. and Packard, A. and Seiler, P. and Wheeler, T.},
booktitle={American Control Conference, 2007. ACC ’07},
year={2007},
month={July},
volume={},
number={},
pages={6009-6014},
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.},
keywords={Lyapunov methods, linear programming, polynomials, search problems, stability, vectorsLyapunov function candidates, ROA invariant subsets, bilinear constraints, bilinear search strategies, finite dimensional polynomial parameterizations, linear sum-of-squares optimization problems, polynomial vector fields, region-of-attraction, simulations, stability region analysis, sum-of-squares programming},
doi={10.1109/ACC.2007.4283013},
ISSN={0743-1619},
}