### 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 : Nonlinear and Hybrid Control Systems |

Editors | M.K. Camlibel, A.A. Julius, R. Pasumarthy, J.M.A. Scherpen |

Place of Publication | Dordrecht |

Publisher | Springer |

Pages | 343-348 |

Number of pages | 6 |

ISBN (Electronic) | 978-3-319-20988-3 |

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

DOIs | |

Publication status | Published - 2015 |

Event | Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear Control, 12-13 July 2015, Groningen, The Netherlands - Jan C. Willems Center for Systems and Control at the University of Groningen, Groningen, Netherlands Duration: 12 Jul 2015 → 13 Jul 2015 |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 461 |

ISSN (Print) | 0170-8643 |

### Conference

Conference | Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear Control, 12-13 July 2015, Groningen, The Netherlands |
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Country | Netherlands |

City | Groningen |

Period | 12/07/15 → 13/07/15 |

### Cite this

*Mathematical Control Theory I : Nonlinear and Hybrid Control Systems*(pp. 343-348). (Lecture Notes in Control and Information Sciences; Vol. 461). Dordrecht: Springer. https://doi.org/10.1007/978-3-319-20988-3_18

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*Mathematical Control Theory I : Nonlinear and Hybrid Control Systems.*Lecture Notes in Control and Information Sciences, vol. 461, Springer, Dordrecht, pp. 343-348, Workshop on Mathematical Systems Theory: From Behaviors to Nonlinear Control, 12-13 July 2015, Groningen, The Netherlands, Groningen, Netherlands, 12/07/15. https://doi.org/10.1007/978-3-319-20988-3_18

**Examples on stability for infinite-dimensional systems.** / Zwart, H.J.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Examples on stability for infinite-dimensional systems

AU - Zwart, H.J.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84983540212&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-20988-3_18

DO - 10.1007/978-3-319-20988-3_18

M3 - Chapter

AN - SCOPUS:84983540212

SN - 978-3-319-20987-6

T3 - Lecture Notes in Control and Information Sciences

SP - 343

EP - 348

BT - Mathematical Control Theory I : Nonlinear and Hybrid Control Systems

A2 - Camlibel, M.K.

A2 - Julius, A.A.

A2 - Pasumarthy, R.

A2 - Scherpen, J.M.A.

PB - Springer

CY - Dordrecht

ER -