Title page for ETD etd-05112006-154752
|Type of Document
||Kang, Jeongook Kim
||Interpolation by rational matrix functions with minimal McMillan degree
|Ball, Joseph A.
|Hannsgen, Kenneth B.
|Herdman, Terry L.
|Kohler, Werner E.
|Thomson, James E.
|Date of Defense
Interpolation conditions on rational matrix functions expressed in terms of residues
are studied. As a compact way of expressing tangential interpolation conditions of
arbitrarily high multiplicity possibly from both sides simultaneously, interpolation
conditions are represented in terms of residues. The minimal possible complexity,
measured by the McMillan degree, of interpolants is found in terms of the controllability
and the observability indices of certain pairs of matrices which are part of
given data. An interpolant of such complexity is obtained in realization form. This
leads to another approach to the partial realization problem. As a generalization of
the well-known Lagrange interpolation problem for scalar polynomials, the problem
of seeking for a matrix polynomial interpolant of low complexity is studied. The
main tool is state space methods borrowed from systems theory. After adoption of
state space methods, problems concerning rational matrix functions are reduced to
the realm of linear algebra.
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