Antoulas, Athanasios C.2018-12-032018-12-032008Mayo, Andrew. "Generalized realization." (2008) Diss., Rice University. <a href="https://hdl.handle.net/1911/103589">https://hdl.handle.net/1911/103589</a>.https://hdl.handle.net/1911/103589This thesis is broadly concerned with the following problem: given frequency response measurements construct a linear time-invariant system that is consistent with these measurements. This problem arises, for example, in V.L.S.I. design and testing. The major contribution of this thesis is to provide a new solution to this problem in which the celebrated Silverman-Ho algorithm is shown to be a special case. The major difference between this method and existing methods is the use of the shifted Loewner matrix in addition to the Loewner matrix. The approach advocated is then extended to deal with inexact data and rational approximation. The error introduced in these scenarios is analyzed. Finally, some progress is made in the "permissible order" problem of rational interpolation. The permissible orders of interpolants are shown to be related to the Kronecker structure of the matrix pencil associated to the Loewner and shifted Loewner matrices.94 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Electrical engineeringApplied sciencesDescriptor systemsGeneralized realizationIdentificationInterpolationLoewner matricesThesis304509864THESIS E.E. 2009 MAYO