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

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 L_∞ noise model. In the noise-free open-loop case, the model/data consistency problem boils down to the existence of an interpolating function in ℛℋ_∞ 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 ℛℋ_∞ 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 L_∞ noise corrupting the frequency-response measurements, a complete solution to the open-loop noisy SISO problem using the structured singular value μ is given