### Abstract

Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be difficult to characterize and are sometimes ill-posed. However, for this class of systems the zero dynamics are shown to be well-defined. Using the underlying structure, simple characterizations and a constructive procedure can be obtained.

Original language | Undefined |
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Title of host publication | 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015 |

Publisher | IFAC Proceedings |

Pages | 241-243 |

Number of pages | 3 |

ISBN (Print) | 2405-8963 |

DOIs | |

Publication status | Published - 2015 |

Event | 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015 - Lyon, France Duration: 6 Jul 2015 → 7 Jul 2015 Conference number: 5 |

### Publication series

Name | |
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Publisher | IFAC Proceedings |

Number | 13 |

Volume | 48 |

ISSN (Print) | 2405-8963 |

### Workshop

Workshop | 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015 |
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Abbreviated title | LHMNC |

Country | France |

City | Lyon |

Period | 6/07/15 → 7/07/15 |

### Keywords

- coupled wave equations
- EWI-26572
- zero dynamics
- Port-Hamiltonian system
- METIS-315602
- Distributed-parameter systems
- IR-99328
- Boundary control
- Networks

## Cite this

Zwart, H. J. (2015). Using System Theory and Energy Methods to Prove Existence of Non-linear PDE's. In

*5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, LHMNC 2015*(pp. 241-243). IFAC Proceedings. https://doi.org/10.1016/j.ifacol.2015.10.246