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Consistency of Open-Loop Experimental
Frequency-Response Data with Coprime Factor Plant Models

The model/data consistency problem for coprime factorizations considered
in this research is the following: Given some possibly noisy frequency-response
data obtained by running open-loop experiments on a system, show that these
data are consistent with a given family of perturbed coprime factor models
and a time-domain
noise model. In the noise-free open-loop case, the model/data consistency
problem boils down to the existence of an interpolating function in
that evaluates to a finite number of complex matrices at a finite number
of points on the imaginary axis. A theorem on boundary interpolation in
is a building block that allows us to devise computationally simple, necessary
and sufficient tests to check if the perturbed coprime factorization is
consistent with the data. For standard coprime factorizations, the test
involves the computation of minimum-norm solutions to overdetermined complex
matrix equations. The Schmidt-Mirsky Theorem is used in the case of special
factorizations of flexible systems. For
noise corrupting the frequency-response measurements, a complete solution
to the open-loop noisy SISO problem using the structured singular value
is given.
*B. Boulet, B. A. Francis*

*Annual Report*

*Mon Jun 26 21:22:20 GMT 2000*