SM identification of approximating models for HINF robust control

Set Membership (SM) H∞ identification of mixed parametric and nonparametric models is investigated, aimed to estimate a low order approximating model and an identification error, giving a measure of the unmodeled dynamics in a form well suited for H∞ control methodologies. In particular, the problem of estimating the parameters of the parametric part and the H∞ bound on the modeling error is solved using frequency domain data, supposing l∞ bounded measurement errors and exponentially stable unmodeled dynamics. The effectiveness of the proposed procedure is tested on some numerical examples, showing the advantages of the proposed methods over the existing nonparametric H∞ identification approaches are shown, in terms of lower model order and of tightness in the modeling error bounds.