Type of Document Dissertation Author Kang, Jeongook Kim URN etd-05112006-154752 Title Interpolation by rational matrix functions with minimal McMillan degree Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Ball, Joseph A. Committee Chair Hannsgen, Kenneth B. Committee Member Herdman, Terry L. Committee Member Kohler, Werner E. Committee Member Thomson, James E. Committee Member Keywords

- Interpolation Research
Date of Defense 1990-12-05 Availability restricted AbstractInterpolation 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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