Consistency of open-loop experimental frequency-response data with coprime factor plant models

Abstract

The model/data consistency problem for coprime factorization considered is: 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 /spl Lscr//sub /spl infin// noise model. In the noise-free open-loop case, the model/data consistency problem boils down to the existence of an interpolating function in /spl Rscr//spl Hscr//sub /spl infin// 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 /spl Rscr//spl Hscr//sub /spl infin// is a building block that allows one 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 underdetermined complex matrix equations. The Schmidt-Mirsky theorem is used in the case of special factorizations of flexible systems. For /spl Lscr//sub /spl infin// noise corrupting the frequency-response measurements, a complete solution to the open-loop noisy SISO problem using the structured singular value /spl mu/ is given.