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**Decentralized observers with consensus filters for distributed discrete-time linear systems.**
*(English)*
Zbl 1298.93072

Summary: This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtain a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.

### MSC:

93B07 | Observability |

93A14 | Decentralized systems |

93C55 | Discrete-time control/observation systems |

93C05 | Linear systems in control theory |

05C90 | Applications of graph theory |

93E10 | Estimation and detection in stochastic control theory |

93E11 | Filtering in stochastic control theory |

68T42 | Agent technology and artificial intelligence |

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\textit{B. Açıkmeşe} et al., Automatica 50, No. 4, 1037--1052 (2014; Zbl 1298.93072)

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