Computation of signature symmetric balanced realizations

U. Helmke; K. Hüper; J. B. Moore

doi:10.1023/A:1024822603531

Computation of signature symmetric balanced realizations

U. Helmke^*, K. Hüper, J. B. Moore

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of the algorithm is shown.

Original language	English
Pages (from-to)	135-148
Number of pages	14
Journal	Journal of Global Optimization
Volume	27
Issue number	2-3
DOIs	https://doi.org/10.1023/A:1024822603531
Publication status	Published - Nov 2003

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title = "Computation of signature symmetric balanced realizations",

abstract = "A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of the algorithm is shown.",

keywords = "Balancing, Cost function, Jacobi method, Quadratic convergence, Signature symmetric realizations",

author = "U. Helmke and K. H{\"u}per and Moore, {J. B.}",

year = "2003",

month = nov,

doi = "10.1023/A:1024822603531",

language = "English",

volume = "27",

pages = "135--148",

journal = "Journal of Global Optimization",

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publisher = "Springer Netherlands",

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TY - JOUR

T1 - Computation of signature symmetric balanced realizations

AU - Helmke, U.

AU - Hüper, K.

AU - Moore, J. B.

PY - 2003/11

Y1 - 2003/11

N2 - A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of the algorithm is shown.

AB - A new numerical scheme for computing balancing coordinate transformations for signature symmetric realizations in linear systems theory is presented. The method is closely related to the Jacobi method for diagonalizing symmetric matrices. Here the minimization of the sum of traces of the Gramians by orthogonal and hyperbolic Jacobi-type rotations is considered. Local quadratic convergence of the algorithm is shown.

KW - Balancing

KW - Cost function

KW - Jacobi method

KW - Quadratic convergence

KW - Signature symmetric realizations

UR - http://www.scopus.com/inward/record.url?scp=0042929901&partnerID=8YFLogxK

U2 - 10.1023/A:1024822603531

DO - 10.1023/A:1024822603531

M3 - Article

SN - 0925-5001

VL - 27

SP - 135

EP - 148

JO - Journal of Global Optimization

JF - Journal of Global Optimization

IS - 2-3

ER -

Computation of signature symmetric balanced realizations

Abstract

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