### Abstract

This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-of-Squares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

Original language | English |
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Title of host publication | Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC) |

Editors | Francesco Bullo, Christophe Prieur, Alessandro Giua |

Place of Publication | Piscataway, NJ, USA |

Publisher | IEEE |

Pages | 3892-3897 |

ISBN (Electronic) | 978-1-5090-1837-6 |

DOIs | |

Publication status | Published - 2016 |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: 12 Dec 2016 → 14 Dec 2016 |

### Conference

Conference | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Abbreviated title | CDC 2016 |

Country | United States |

City | Las Vegas |

Period | 12/12/16 → 14/12/16 |

### Keywords

- Output feedback
- Optimization
- Nonlinear systems
- Iterative methods
- Convergence
- Lyapunov methods
- Symmetric matrices

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## Cite this

*Proceedings of the 2016 IEEE 55th Conference on Decision and Control (CDC)*(pp. 3892-3897). [7798857] IEEE. https://doi.org/10.1109/CDC.2016.7798857