Model validation of multirate systems from time-domain experimental data

The model validation problem using time-domain experimental data is studied for multirate linear fractional uncertain models in this note. As a technical tool, the Carathéodory-Fejér (CF) interpolation problem with a nest operator constraint is first investigated. This problem is itself of interest mathematically and has potential applications in addressing other problems in control, signal processing, and circuit theory. A necessary and sufficient solvability condition for this interpolation problem is given. The validation tests are then presented based on this condition and the lifting technique. Tractable convex optimization methods can be used to solve the validation problems.