Input-output stability of linear consensus processes

Ji Liu, Tamer Basar, Angelia Nedich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6978-6983
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Externally publishedYes
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

Fingerprint

Linear equations
Output
Differential equations
Asymptotic stability
Recursion
Linear systems
Column vector
Local Interaction
Seminorm
Linear differential equation
Continuous Time
Discrete-time
Linear Systems
Differential equation
Perturbation
Sufficient Conditions

ASJC Scopus subject areas

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

Cite this

Liu, J., Basar, T., & Nedich, A. (2016). Input-output stability of linear consensus processes. In 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.

2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 6978-6983 7799344.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Liu, J, Basar, T & Nedich, A 2016, Input-output stability of linear consensus processes. in 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
Liu J, Basar T, Nedich A. Input-output stability of linear consensus processes. In 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 6978-6983. 7799344 https://doi.org/10.1109/CDC.2016.7799344
Liu, Ji ; Basar, Tamer ; Nedich, Angelia. / Input-output stability of linear consensus processes. 2016 IEEE 55th Conference on Decision and Control, CDC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 6978-6983
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