Distributed Estimation of All the Eigenvalues and Eigenvectors of Matrices Associated With Strongly Connected Digraphs

Gusrialdi, Azwirman; Qu, Zhihua

doi:10.1109/lcsys.2017.2717799

Distributed Estimation of All the Eigenvalues and Eigenvectors of Matrices Associated With Strongly Connected Digraphs

Journal Article · Tue Jun 20 00:00:00 EDT 2017 · IEEE Control Systems Letters

DOI:https://doi.org/10.1109/lcsys.2017.2717799· OSTI ID:1820235

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Univ. of Central Florida, Orlando, FL (United States); University of Central Florida
Univ. of Central Florida, Orlando, FL (United States)

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, in this work 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.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Central Florida, Orlando, FL (United States)

Sponsoring Organization:: USDOE Office of Energy Efficiency and Renewable Energy (EERE); USDOT; National Science Foundation (NSF); L-3 Communication; Leidos

Grant/Contract Number:: EE0007998; EE0006340; EE0007327

OSTI ID:: 1820235

Journal Information:: IEEE Control Systems Letters, Journal Name: IEEE Control Systems Letters Journal Issue: 2 Vol. 1; ISSN 2475-1456

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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