### 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) |
---|---|

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 |
---|---|

Country | United States |

City | Las Vegas |

Period | 12/12/16 → 12/14/16 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*2016 IEEE 55th Conference on Decision and Control, CDC 2016*(pp. 6978-6983). [7799344] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2016.7799344

**Input-output stability of linear consensus processes.** / Liu, Ji; Basar, Tamer; Nedich, Angelia.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2016 IEEE 55th Conference on Decision and Control, CDC 2016.*, 7799344, Institute of Electrical and Electronics Engineers Inc., pp. 6978-6983, 55th IEEE Conference on Decision and Control, CDC 2016, Las Vegas, United States, 12/12/16. https://doi.org/10.1109/CDC.2016.7799344

}

TY - GEN

T1 - Input-output stability of linear consensus processes

AU - Liu, Ji

AU - Basar, Tamer

AU - Nedich, Angelia

PY - 2016/12/27

Y1 - 2016/12/27

N2 - 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 Rn 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.

AB - 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 Rn 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.

UR - http://www.scopus.com/inward/record.url?scp=85010824749&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85010824749&partnerID=8YFLogxK

U2 - 10.1109/CDC.2016.7799344

DO - 10.1109/CDC.2016.7799344

M3 - Conference contribution

SP - 6978

EP - 6983

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -