### Abstract

By means of examples, we study stability of infinite-dimensional linear and nonlinear systems. First we show that having a (strict) Lyapunov function does not imply asymptotic stability, even not for linear systems. Second, we show that to conclude (local) exponential stability from the linearization, care must be taken how the linearization is obtained.

Original language | English |
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Title of host publication | Mathematical Control Theory I |

Editors | M. Kanat Camlibel, R.P. Ramkrishna Pasumarthy, A. Agung Julius, Jacquelien M.A. Scherpen |

Place of Publication | London |

Publisher | Springer |

Pages | 343-348 |

Number of pages | 6 |

ISBN (Print) | 978-3-319-20987-6 |

DOIs | |

Publication status | Published - 14 Jul 2015 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Publisher | Springer Verlag |

Number | 461 |

Volume | 461 |

ISSN (Print) | 0170-8643 |

### Keywords

- MSC-53C38
- MSC-34H05
- METIS-314962
- IR-98399
- EWI-26283

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## Cite this

Zwart, H. J. (2015). Examples on Stability for Infinite-Dimensional Systems. In M. Kanat Camlibel, R. P. Ramkrishna Pasumarthy, A. Agung Julius, & J. M. A. Scherpen (Eds.),

*Mathematical Control Theory I*(pp. 343-348). (Lecture Notes in Control and Information Sciences; Vol. 461, No. 461). London: Springer. https://doi.org/10.1007/978-3-319-20988-3_18