Input-output stability of linear consensus processes

Ji Liu; Tamer Basar; Angelia Nedic

doi:10.1109/CDC.2016.7799344

Input-output stability of linear consensus processes

Ji Liu, Tamer Basar, Angelia Nedic

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

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 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.

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	https://doi.org/10.1109/CDC.2016.7799344
State	Published - Dec 27 2016
Event	55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States Duration: Dec 12 2016 → Dec 14 2016

Publication series

Name	2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other	55th IEEE Conference on Decision and Control, CDC 2016
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 12/14/16

ASJC Scopus subject areas

Artificial Intelligence
Decision Sciences (miscellaneous)
Control and Optimization

Online availability

10.1109/CDC.2016.7799344

Library availability

Discover UIUC Full Text

Cite this

Input-output stability of linear consensus processes. / Liu, Ji; Basar, Tamer; Nedic, Angelia.
2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 6978-6983 7799344 (2016 IEEE 55th Conference on Decision and Control, CDC 2016).

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

Liu, J, Basar, T & Nedic, A 2016, Input-output stability of linear consensus processes. in 2016 IEEE 55th Conference on Decision and Control, CDC 2016., 7799344, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, 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

@inproceedings{4f23b6d926194eaa8c763efcb488a6a8,

title = "Input-output stability of linear consensus processes",

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 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.",

author = "Ji Liu and Tamer Basar and Angelia Nedic",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 55th IEEE Conference on Decision and Control, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

year = "2016",

month = dec,

day = "27",

doi = "10.1109/CDC.2016.7799344",

language = "English (US)",

series = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "6978--6983",

booktitle = "2016 IEEE 55th Conference on Decision and Control, CDC 2016",

address = "United States",

}

TY - GEN

T1 - Input-output stability of linear consensus processes

AU - Liu, Ji

AU - Basar, Tamer

AU - Nedic, 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

AN - SCOPUS:85010824749

T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

SP - 6978

EP - 6983

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

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 55th IEEE Conference on Decision and Control, CDC 2016

Y2 - 12 December 2016 through 14 December 2016

ER -

Input-output stability of linear consensus processes

Abstract

Publication series

Other

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this