### Abstract

In this paper, we design an exponentially convergent distur- bance observer for a wave PDE on a time-varying domain by using two boundary measurements u(0; t); ut(l(t); t). More speci-cally, two auxiliary PDEs are constructed to build the disturbance observer for tracking the external disturbance in the wave PDE. Exponential convergence of the disturbance estimation to the true disturbance value is proved by Lya- punov analysis, and all states in the observer are shown to be bounded once the original state u(x; t) is bounded via designing control input.

Original language | English |
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Title of host publication | Proceedings of the SIAM Conference on Control and Its Applications, CT 2017 |

Editors | Ruihua Liu, Qing Zhang, Wei Kang, Jean-Pierre Barbot |

Publisher | Society for Industrial and Applied Mathematics Publications |

Pages | 107-111 |

Number of pages | 5 |

ISBN (Electronic) | 9781611975000 |

State | Published - 2017 |

Event | 2017 SIAM Conference on Control and Its Applications, CT 2017 - Pittsburgh, United States Duration: Jul 10 2017 → Jul 12 2017 |

### Publication series

Name | Proceedings of the SIAM Conference on Control and Its Applications, CT 2017 |
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### Conference

Conference | 2017 SIAM Conference on Control and Its Applications, CT 2017 |
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Country | United States |

City | Pittsburgh |

Period | 07/10/17 → 07/12/17 |

## Cite this

Wang, J., Tang, S. X., Pi, Y., & Krstic, M. (2017). Disturbance Estimation of a Wave PDE on a Time-varying Domain. In R. Liu, Q. Zhang, W. Kang, & J-P. Barbot (Eds.),

*Proceedings of the SIAM Conference on Control and Its Applications, CT 2017*(pp. 107-111). (Proceedings of the SIAM Conference on Control and Its Applications, CT 2017). Society for Industrial and Applied Mathematics Publications.