### Optimization and Systems Theory Seminar

Friday, September 15, 2000, 11.00-12.00, Room 3721, Lindstedtsvägen 25

** Professor
György Michaletzky **

Deptartment of Probability Theory and Statistics

Eötvös Loránd University

Budapest, Hungary

E-mail: michgy@ludens.elte.hu

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On the reduced rank Nevanlinna-Pick interpolation problem

In this talk we consider the Nevanlinna-Pick interpolation problem
but instead of contractive, analytic functions so-called
positive real functions will be studied. There are several
equivalent formulations of this problem, e.g. in terms of zero
structure, covariant extension.
Using the linear fractional parameterization of all solutions
of the interpolation problem formulated on the right half-plane
the input functions providing solutions with McMillan-degree
less than the number of interpolation nodes will be
characterized.

Using the covariance extension formulation we show that the
interpolation problem formulated on the unit disc can be
transformed into an orthogonality condition directly leading to a
characterization of all solutions. State-space forms of the
generalized Kimura-Georgiou-parameterization will be provided,
as well.

Calendar of seminars

*Last update: September 11, 2000 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*