### Abstract

A general framework for Region of Attraction (ROA) analysis is presented. The considered system consists of the feedback interconnection of a plant with polynomial dynamics and a bounded operator. The input/output behavior of the latter is characterized using an Integral Quadratic Constraint (IQC), for which it is assumed an hard factorization holds. This formulation allows to analyze problems involving hard-nonlinearities and uncertainties, adding to the state of practice typically limited to polynomial vector fields. An iterative algorithm based on Sum of Squares optimization is proposed to compute inner estimates of the ROA. The effectiveness of this approach is demonstrated on a numerical example featuring a nonlinear closed-loop system with saturated inputs.

Original language | English (US) |
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Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3922-3927 |

Number of pages | 6 |

ISBN (Electronic) | 9781538613955 |

DOIs | |

State | Published - Jan 18 2019 |

Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 2018-December |

ISSN (Print) | 0743-1546 |

### Conference

Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
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Country | United States |

City | Miami |

Period | 12/17/18 → 12/19/18 |

### Fingerprint

### Cite this

*2018 IEEE Conference on Decision and Control, CDC 2018*(pp. 3922-3927). [8619669] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619669

**Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints.** / Iannelli, Andrea; Seiler, Peter; Marcos, Andres.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2018 IEEE Conference on Decision and Control, CDC 2018.*, 8619669, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 3922-3927, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619669

}

TY - GEN

T1 - Estimating the Region of Attraction of Uncertain Systems with Integral Quadratic Constraints

AU - Iannelli, Andrea

AU - Seiler, Peter

AU - Marcos, Andres

PY - 2019/1/18

Y1 - 2019/1/18

N2 - A general framework for Region of Attraction (ROA) analysis is presented. The considered system consists of the feedback interconnection of a plant with polynomial dynamics and a bounded operator. The input/output behavior of the latter is characterized using an Integral Quadratic Constraint (IQC), for which it is assumed an hard factorization holds. This formulation allows to analyze problems involving hard-nonlinearities and uncertainties, adding to the state of practice typically limited to polynomial vector fields. An iterative algorithm based on Sum of Squares optimization is proposed to compute inner estimates of the ROA. The effectiveness of this approach is demonstrated on a numerical example featuring a nonlinear closed-loop system with saturated inputs.

AB - A general framework for Region of Attraction (ROA) analysis is presented. The considered system consists of the feedback interconnection of a plant with polynomial dynamics and a bounded operator. The input/output behavior of the latter is characterized using an Integral Quadratic Constraint (IQC), for which it is assumed an hard factorization holds. This formulation allows to analyze problems involving hard-nonlinearities and uncertainties, adding to the state of practice typically limited to polynomial vector fields. An iterative algorithm based on Sum of Squares optimization is proposed to compute inner estimates of the ROA. The effectiveness of this approach is demonstrated on a numerical example featuring a nonlinear closed-loop system with saturated inputs.

UR - http://www.scopus.com/inward/record.url?scp=85062177293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062177293&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619669

DO - 10.1109/CDC.2018.8619669

M3 - Conference contribution

AN - SCOPUS:85062177293

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3922

EP - 3927

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -