### Abstract

Original language | English |
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Title of host publication | Proceedings of the 10th international conference on Hybrid systems: computation and control (HSCC 2007) 3 - 5 April 2007, Pisa, Italy |

Editors | A. Bemporard, A. Bicchi, G. Buttazzo |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 259-272 |

ISBN (Print) | 978-3-540-71492-7 |

DOIs | |

Publication status | Published - 2007 |

Event | 10th International Conference on Hybrid Systems: Computation and Control (HSCC 2007) - Pisa, Italy Duration: 3 Apr 2007 → 5 Apr 2007 Conference number: 10 http://cse.lab.imtlucca.it/~bemporad/hybrid/hscc07/ |

### Publication series

Name | Lecture Notes in Computer Science |
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Volume | 4416 |

ISSN (Print) | 0302-9743 |

### Conference

Conference | 10th International Conference on Hybrid Systems: Computation and Control (HSCC 2007) |
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Abbreviated title | HSCC 2007 |

Country | Italy |

City | Pisa |

Period | 3/04/07 → 5/04/07 |

Internet address |

### Fingerprint

### Cite this

*Proceedings of the 10th international conference on Hybrid systems: computation and control (HSCC 2007) 3 - 5 April 2007, Pisa, Italy*(pp. 259-272). (Lecture Notes in Computer Science; Vol. 4416). Berlin: Springer. https://doi.org/10.1007/978-3-540-71493-4_22

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*Proceedings of the 10th international conference on Hybrid systems: computation and control (HSCC 2007) 3 - 5 April 2007, Pisa, Italy.*Lecture Notes in Computer Science, vol. 4416, Springer, Berlin, pp. 259-272, 10th International Conference on Hybrid Systems: Computation and Control (HSCC 2007), Pisa, Italy, 3/04/07. https://doi.org/10.1007/978-3-540-71493-4_22

**Input-to-state stability of discontinuous dynamical systems with an observer-based control application.** / Heemels, W.P.M.H.; Weiland, S.; Juloski, A.

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

TY - GEN

T1 - Input-to-state stability of discontinuous dynamical systems with an observer-based control application

AU - Heemels, W.P.M.H.

AU - Weiland, S.

AU - Juloski, A.

PY - 2007

Y1 - 2007

N2 - In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov's solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that ``multiple Lyapunov functions'' are commonly used in the stability theory for hybrid systems. We will show that the existence of a non-smooth (but Lipschitz continuous) ISS Lyapunov function for a discontinuous system implies ISS. Next, we will prove an ISS interconnection theorem for two discontinuous dynamical systems that both admit an ISS Lyapunov function. The interconnection will be shown to be globally asymptotically stable under a small gain condition. The developed ISS theory will be applied to observer-based controller design for a class of piecewise linear systems using an observer structure proposed by the authors. The LMI-based design of the state feedback and the observer can be performed separately.

AB - In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov's solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that ``multiple Lyapunov functions'' are commonly used in the stability theory for hybrid systems. We will show that the existence of a non-smooth (but Lipschitz continuous) ISS Lyapunov function for a discontinuous system implies ISS. Next, we will prove an ISS interconnection theorem for two discontinuous dynamical systems that both admit an ISS Lyapunov function. The interconnection will be shown to be globally asymptotically stable under a small gain condition. The developed ISS theory will be applied to observer-based controller design for a class of piecewise linear systems using an observer structure proposed by the authors. The LMI-based design of the state feedback and the observer can be performed separately.

U2 - 10.1007/978-3-540-71493-4_22

DO - 10.1007/978-3-540-71493-4_22

M3 - Conference contribution

SN - 978-3-540-71492-7

T3 - Lecture Notes in Computer Science

SP - 259

EP - 272

BT - Proceedings of the 10th international conference on Hybrid systems: computation and control (HSCC 2007) 3 - 5 April 2007, Pisa, Italy

A2 - Bemporard, A.

A2 - Bicchi, A.

A2 - Buttazzo, G.

PB - Springer

CY - Berlin

ER -