Input-output stability of linear consensus processes

Ji Liu; Tamer Basar; Angelia Nedich

doi:10.1109/CDC.2016.7799344

Input-output stability of linear consensus processes

Ji Liu, Tamer Basar, Angelia Nedich

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

4 Scopus citations

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
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/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

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10.1109/CDC.2016.7799344

Cite this

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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 Nedich",

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month = dec,

day = "27",

doi = "10.1109/CDC.2016.7799344",

language = "English (US)",

pages = "6978--6983",

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

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note = "55th IEEE Conference on Decision and Control, CDC 2016 ; Conference date: 12-12-2016 Through 14-12-2016",

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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.

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DO - 10.1109/CDC.2016.7799344

M3 - Conference contribution

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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

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ER -

Input-output stability of linear consensus processes

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