On the consistency between an LFT described model set and frequency domain data

The main objective of this technical note is to derive a simple necessary and sufficient condition for a linear fractional transformation (LFT) perturbed model set being consistent with frequency domain plant input-output data. Only discrete-time models and unstructured modeling errors are dealt with. Compared with the available results in which the eigenvalues of a matrix are involved, this condition is related only to the Euclidean norms of two vectors. Moreover, these vectors linearly depend on measurement errors. Some of its applications to model set validation have been briefly discussed. Based on this condition, an almost analytic solution has been established for model set validation under a deterministic framework when the measurement errors are energy bounded. Numerical simulations show that this consistency condition can lead to a significant computation cost reduction