### Docent Seminar, Optimization and Systems Theory

Friday, March 10, 2000, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Yishao Zhou**

Stockholm University

E-mail: yishao@matematik.su.se

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Balanced parametrization of a class of positive real functions

In this talk we concentrate on the parametrization of a class of
positive real functions in connection to the spectral factorization
problems, partial realization problems, etc, using the polynomial model.
We will show that the Kimura realization for the so-called ``maximum
entropy solution'' is indeed Riccati balanced parametrization of this
class of positive real functions and the related realization of the
minimum phase spectral factor, Lyapunov balanced. The talk will start
with a general presentation of the polynomial model and orthogonal
polynomials. Then we work out the Kimura realization through the shift
operator using a set of orthonormal polynomials. Linear algebra is the main
tool of our analysis.

Calendar of seminars

*Last update: Mars 2, 2000 by
Petter Ögren,
petter.ogren@math.kth.se.
*