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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 2.3

Aspects of Fisher geometry for stochastic

linear systems

Bernard Hanzon

Institute for Econometrics, Operations Research and System Theory

Technical University of Vienna Argentinierstr. 8/119

Argentinierstr. 8/119

A-1040 Vienna

Austria

bhanzon@eos.tuwien.ac.at

Ralf Peeters

Department of Mathematics

Maastricht University

P.O. Box 616, 6200 MD Maastricht

The Netherlands

ralf.peeters@math.unimaas.nl

1 DESCRIPTION OF THE PROBLEM

Consider the space S of stable minimum phase systems in discrete-time, of order (McMillan degree) n, having m inputs and m outputs, driven by a stationary Gaussian white noise (innovations) process of zero mean and covariance . This space is often considered, for instance in system identification, to characterize ...

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