Necessary conditions for consistency of noise-free, closed-loop frequency-response data with coprime factor models

A basic requirement of robust control theory is that a nominal model and an uncertainty model be available for the plant. The assumption is that the plant can be modeled by at least one of the perturbations of the nominal model in the uncertainty set. This raises the problem of constructing such an uncertainty set that would be consistent with a given set of experimental input-output data. This paper introduces necessary conditions for the model/data consistency problem with coprime factor uncertainty and noise-free closed-loop frequency-response measurements. The necessary conditions involve the computation of singular values of complex matrices associated with the measurement frequencies. Standard factorizations and left-coprime factor models of large flexible space structures are considered