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Cascade analysis and synthesis of transfer functions of infinite dimensional linear systems

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dc.contributor.authorCarpenter, Lon E.en
dc.contributor.committeechairBall, Joseph A.en
dc.contributor.committeememberBurns, John A.en
dc.contributor.committeememberWheeler, Robert L.en
dc.contributor.committeememberRussell, David L.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:16:45Zen
dc.date.adate2008-07-28en
dc.date.available2014-03-14T21:16:45Zen
dc.date.issued1992-06-13en
dc.date.rdate2008-07-28en
dc.date.sdate2008-07-28en
dc.description.abstractProblems of cascade connections (synthesis) and decomposition (analysis) are analyzed for two classes of linear systems with infinite dimensional state spaces, namely, 1) admissible systems in the sense of Bart, Gohberg and Kaashoek and 2) regular systems as recently introduced by Weiss. For the class of BGK-admissible systems, it is shown that the product of two admissible systems is again admissible and that a Wiener-Hopf factorization problem can be solved just as in the finite-dimensional case. For the class of regular systems, it is shown that the cascade connection of a rational stable and antistable system has an additive stable-antistable decomposition; this involves giving a distribution interpretation to the solution of a linear Sylvester equation involving unbounded operator coefficients. As an application, some preliminary work is presented toward obtaining a state space solution of the sensitivity minimization problem for a pure delay plant.en
dc.description.degreePh. D.en
dc.format.extentiv, 86 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-07282008-135307en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07282008-135307/en
dc.identifier.urihttp://hdl.handle.net/10919/38950en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1992.C376.pdfen
dc.relation.isformatofOCLC# 26187430en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1992.C376en
dc.subject.lcshLinear systemsen
dc.subject.lcshTransfer functionsen
dc.titleCascade analysis and synthesis of transfer functions of infinite dimensional linear systemsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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