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Asymptotic unbounded root loci - Formulas and computationA new geometric way of computing the asymptotic behavior of unbounded root loci of a strictly proper linear time-invariant control system as loop gain goes to infinity is presented. Properties of certain restricted linear maps and nested restrictions of linear maps are developed, and formulas are obtained for the leading coefficient of the asymptotic values of the unbounded multivariable root loci are obtained in terms of eigenvalues of those maps. Published results and a certain simple null structure assumption are used to relate these asymptotic values to the structure at infinity of the Smith-McMillan form of the open loop transfer function. Explicit matrix formulas for the more abstract derived formulas are given and additional geometric insights are developed with orthogonal projections and singular value decomposition. Formulas for the pivots of the unbounded root loci are calculated and shown to have the same form as the coefficients of the unbounded asymptotic root loci.
Document ID
19830056330
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Sastry, S. S.
(California Univ. Berkeley, CA, United States)
Desoer, C. A.
(California, University Berkeley, CA, United States)
Date Acquired
August 11, 2013
Publication Date
May 1, 1983
Publication Information
Publication: IEEE Transactions on Automatic Control
Volume: AC-28
ISSN: 0018-9286
Subject Category
Numerical Analysis
Accession Number
83A37548
Funding Number(s)
CONTRACT_GRANT: NSF ENG-78-09032-A01
CONTRACT_GRANT: NGL-22-009-124
Distribution Limits
Public
Copyright
Other

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