### Abstract

Finite-time stability (FTS) requires that the state of a system does not exceed a certain bound during a specified time interval for given bound on the initial state. The concept of FTS introduced exogenous inputs is called finite time boundedness (FTB). This paper gives necessary and sufficient conditions for FTB of linear time-varying continuous-time systems. The conditions are extensions of existing necessary and sufficient for FTS. The sufficient conditions for FTB are also given in terms of differential linear matrix inequalities, which can be relaxed by matrix sum of squares, univariate polynomials. Numerical examples show the solvability of the sufficient conditions.

Original language | English |
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Title of host publication | Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 |

Pages | 3214-3219 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 1 Dec 2009 |

Event | 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 15 Dec 2009 → 18 Dec 2009 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### Conference

Conference | 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 |
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Country | China |

City | Shanghai |

Period | 15/12/09 → 18/12/09 |

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## Cite this

*Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009*(pp. 3214-3219). [5400748] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2009.5400748