Distributed Estimation Of All The Eigenvalues And Eigenvectors Of Matrices Associated With Strongly Connected Digraphs

Keywords

Control; Distributed algorithm; Estimation; Irreducible matrix; Network analysis

Abstract

This letter considers the problem of estimating all the eigenvalues and eigenvectors of an irreducible matrix, corresponding to a strongly connected digraph, in the absence of knowledge on the global network topology. To this end, we propose a unified distributed strategy performed by each node in the network and relies only on the local information. The key idea is to transform the nonlinear problem of computing both the eigenvalues and eigenvectors of an irreducible matrix into a linear one. Specifically, we first transform distributively the irreducible matrix into a nonsingular irreducible matrix. Each node in the network then estimates in a distributed fashion the inverse of the nonsingular matrix by solving a set of linear equations based on a consensus-type algorithm. The eigenvalues and the corresponding eigenvectors are finally computed by exploiting the relations between the eigenvalues and eigenvectors of both the inverse and the original irreducible matrices. A numerical example is provided to demonstrate the effectiveness of the proposed distributed strategy.

Publication Date

10-1-2017

Publication Title

IEEE Control Systems Letters

Volume

1

Issue

2

Number of Pages

328-333

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1109/LCSYS.2017.2717799

Socpus ID

85052976983 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85052976983

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