### Abstract

This paper presents a proof that the use of polynomial Lyapunov functions is not conservative for studying exponential stability properties of nonlinear ordinary differential equations on bounded regions. The main result implies that if there exists an n-times continuously differentiable Lyapunov function which proves exponential decay on a bounded subset of R-n, then there exists a polynomial Lyapunov function which proves that same rate of decay on the same region. Our investigation is motivated by the use of semidefinite programming to construct polynomial Lyapunov functions for delayed and nonlinear systems of differential equations.

Original language | English (US) |
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Title of host publication | Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC |

Edition | 1 PART 1 |

DOIs | |

State | Published - Dec 1 2008 |

Externally published | Yes |

Event | 17th World Congress, International Federation of Automatic Control, IFAC - Seoul, Korea, Republic of Duration: Jul 6 2008 → Jul 11 2008 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Number | 1 PART 1 |

Volume | 17 |

ISSN (Print) | 1474-6670 |

### Other

Other | 17th World Congress, International Federation of Automatic Control, IFAC |
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Country | Korea, Republic of |

City | Seoul |

Period | 7/6/08 → 7/11/08 |

### Keywords

- Lyapunov methods
- Nonlinear system control
- Stability of NL systems

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*Proceedings of the 17th World Congress, International Federation of Automatic Control, IFAC*(1 PART 1 ed.). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 17, No. 1 PART 1). https://doi.org/10.3182/20080706-5-KR-1001.2875