Browsing by Author "Mayo, Andrew"

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    A behavioral approach to positive interpolation
    (2005) Mayo, Andrew; Antoulas, Athanasios C.
    We study interpolation by positive functions from a behavioural point of view. In particular, by considering the notion of mirror image data, the interpolation problem with passivity constraint is transformed into an unconstrained behavioural modeling one. It will be shown that the generating system for this problem has to be unitary with respect to an indefinite matrix. Using this approach, several results in the theory of interpolation by positive functions are derived in a very natural manner. The use of generating systems leads in a natural way to the recent results obtained by Byrnes et al concerning parametrizing the set of interpolants by the spectral zeros. We then apply the same approach to interpolation on the boundary.
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    Generalized realization
    (2008) Mayo, Andrew; Antoulas, Athanasios C.
    This 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.