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Avtomat. i Telemekh., 2019, Issue 5, Pages 3–31 (Mi at15280)  

Surveys

Consensus in asynchronous multiagent systems. II. Method of joint spectral radius

V. S. Kozyakinab, N. A. Kuznetsovbc, P. Yu. Chebotarevcbd

a Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
b Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow, Russia
c Moscow Institute of Physics and Technology, Moscow, Russia
d Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: We describe mathematical methods for analyzing the stability, stabilizability and consensus of linear multiagent systems with discrete time. These methods are based on the idea of using the notion of joint/generalized spectral radius of matrix sets to analyze the rate of convergence of matrix products with factors from the sets of matrices with special properties. This is a continuation of the survey by the same authors named “Consensus in Asynchronous Multiagent Systems”; the first part was published in [1].

Keywords: asynchronous multiagent systems, consensus, stability, stabilizability, Markov systems, matrix products, joint spectral radius.

Funding Agency Grant Number
Russian Science Foundation 16-11-00063
Russian Academy of Sciences - Federal Agency for Scientific Organizations 30
The work of the third author was partially supported by the program of the Presidium of the Russian Academy of Sciences no. 30 “Theory and Technology of Multi-Level Decentralized Group Control in Conditions of Conflict and Cooperation.”


DOI: https://doi.org/10.1134/S0005231019050015

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English version:
Automation and Remote Control, 2019, 80:5, 791–812

Bibliographic databases:

Document Type: Article
Presented by the member of Editorial Board: A. L. Fradkov

Received: 17.09.2018
Revised: 22.10.2018
Accepted: 08.11.2018

Citation: V. S. Kozyakin, N. A. Kuznetsov, P. Yu. Chebotarev, “Consensus in asynchronous multiagent systems. II. Method of joint spectral radius”, Avtomat. i Telemekh., 2019, no. 5, 3–31; Autom. Remote Control, 80:5 (2019), 791–812

Citation in format AMSBIB
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\paper Consensus in asynchronous multiagent systems. II.~Method of joint spectral radius
\jour Avtomat. i Telemekh.
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\issue 5
\pages 3--31
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\crossref{https://doi.org/10.1134/S0005231019050015}
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