### Abstract

This paper introduces the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights, with the objective of preventing observability of some modes of the network dynamics. Our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the controllability and observability radius of linear systems. We propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from a given set of sensor nodes. We derive optimality conditions and a heuristic optimization algorithm, which we validate through an example.

Original language | English |
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Title of host publication | American Control Conference (ACC), 2016 |

Place of Publication | Piscataway, NJ, USA |

Publisher | IEEE |

Pages | 185-190 |

Number of pages | 6 |

ISBN (Print) | 978-1-4673-8683-8 |

DOIs | |

Publication status | Published - 6 Jul 2016 |

Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: 6 Jul 2016 → 8 Jul 2016 |

### Publication series

Name | |
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Publisher | IEEE |

ISSN (Print) | 2378-5861 |

### Conference

Conference | 2016 American Control Conference, ACC 2016 |
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Abbreviated title | ACC |

Country | United States |

City | Boston |

Period | 6/07/16 → 8/07/16 |

### Keywords

- EWI-27422
- IR-102387
- METIS-319481

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## Cite this

Bianchin, G., Frasca, P., Gasparri, A., & Pasqualetti, F. (2016). The observability radius of network systems. In

*American Control Conference (ACC), 2016*(pp. 185-190). Piscataway, NJ, USA: IEEE. https://doi.org/10.1109/ACC.2016.7524913