### Abstract

In this paper, we show that local exponential stability of a polynomial vector field implies the existence of a Lyapunov function which is a sum-of-squares of polynomials. To do that, we use the Picard iteration. This result shows that local stability of polynomial vector fields can be computed in a relatively efficient manner using semidefinite programming.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Pages | 5949-5954 |

Number of pages | 6 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States Duration: Dec 15 2010 → Dec 17 2010 |

### Other

Other | 2010 49th IEEE Conference on Decision and Control, CDC 2010 |
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Country | United States |

City | Atlanta, GA |

Period | 12/15/10 → 12/17/10 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 5949-5954). [5717536] https://doi.org/10.1109/CDC.2010.5717536

**A converse sum-of-squares Lyapunov result : An existence proof based on the Picard iteration.** / Peet, Matthew; Papachristodoulou, Antonis.

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

*Proceedings of the IEEE Conference on Decision and Control.*, 5717536, pp. 5949-5954, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717536

}

TY - GEN

T1 - A converse sum-of-squares Lyapunov result

T2 - An existence proof based on the Picard iteration

AU - Peet, Matthew

AU - Papachristodoulou, Antonis

PY - 2010

Y1 - 2010

N2 - In this paper, we show that local exponential stability of a polynomial vector field implies the existence of a Lyapunov function which is a sum-of-squares of polynomials. To do that, we use the Picard iteration. This result shows that local stability of polynomial vector fields can be computed in a relatively efficient manner using semidefinite programming.

AB - In this paper, we show that local exponential stability of a polynomial vector field implies the existence of a Lyapunov function which is a sum-of-squares of polynomials. To do that, we use the Picard iteration. This result shows that local stability of polynomial vector fields can be computed in a relatively efficient manner using semidefinite programming.

UR - http://www.scopus.com/inward/record.url?scp=79953156570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953156570&partnerID=8YFLogxK

U2 - 10.1109/CDC.2010.5717536

DO - 10.1109/CDC.2010.5717536

M3 - Conference contribution

AN - SCOPUS:79953156570

SN - 9781424477456

SP - 5949

EP - 5954

BT - Proceedings of the IEEE Conference on Decision and Control

ER -