## 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.

Original language | English (US) |
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Title of host publication | Proceedings of the 2007 American Control Conference, ACC |

Pages | 6009-6014 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2007 |

Event | 2007 American Control Conference, ACC - New York, NY, United States Duration: Jul 9 2007 → Jul 13 2007 |

### Other

Other | 2007 American Control Conference, ACC |
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Country | United States |

City | New York, NY |

Period | 7/9/07 → 7/13/07 |