Frequency-domain tests for validation of linear fractional uncertain models

A frequency domain approach is adopted in this paper to tackle the problem of validating uncertainty models described by linear fractional transforms. This problem amounts to verifying the consistency of certain given mathematical models to experimental information obtained from a physical plant, using either input-output, frequency-domain measurements or frequency samples of the plant. Linear fractional models with both unstructured and structured uncertainties are considered. The problem is resolved in the former case and solved approximately in the latter. Both results lead to tests that are readily computable via convex optimization methods and can be implemented using standard algorithms. In comparison to previously available algorithms based on time-domain information, the main advantage of these tests is that they have a considerably lower level of computational complexity. It is shown that the validation problem reduces to one of Nevanlinna-Pick boundary interpolation, and it can be solved by computing independently a sequence of convex programs of a lower dimension, each of which corresponds to only one frequency sample.