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

The model/data consistency problem for coprime factorizations considered here is this: 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 L-infinity noise model. In the noise-free open-loop case, the model/data consistency problem boils down to the existence of an interpolating function in RHinfinity 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 RHinfinity 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 underdetermined complex matrix equations. The Schmidt-Mirsky theorem is used in the case of special factorizations of flexible systems. For L-infinity noise corrupting the frequency-response measurements, a complete solution to the open-loop noisy single-input/single-output problem using the structured singular value mu is given.