## Abstract

In a network of n agents, consensus means that all n agents reach an agreement on a specific value of some quantity via local interactions. A linear consensus process can typically be modeled by a discrete-time linear recursion equation or a continuous-time linear differential equation, whose equilibria include nonzero states of the form a1 where a is a constant and 1 is a column vector in R^{n} whose entries all equal 1. Using a suitably defined semi-norm, this paper extends the standard notion of input-output stability from linear systems to linear recursions and differential equations of this type. Sufficient conditions for input-output consensus stability are provided. Connections between uniform bounded-input, bounded-output consensus stability and uniform exponential consensus stability are established. Certain types of additive perturbation to a linear consensus process are considered.

Original language | English (US) |
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Title of host publication | 2016 IEEE 55th Conference on Decision and Control, CDC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6978-6983 |

Number of pages | 6 |

ISBN (Electronic) | 9781509018376 |

DOIs | |

State | Published - Dec 27 2016 |

Externally published | Yes |

Event | 55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016 |

### Other

Other | 55th IEEE Conference on Decision and Control, CDC 2016 |
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Country | United States |

City | Las Vegas |

Period | 12/12/16 → 12/14/16 |

## ASJC Scopus subject areas

- Artificial Intelligence
- Decision Sciences (miscellaneous)
- Control and Optimization