H∞ identification of “soft” uncertainty models

The paper investigates the problem of identifying uncertainty models of SISO, LTI, discrete-time, BIBO stable, unknown systems, using frequency domain measurements corrupted by Gaussian noise of known covariance. An additive uncertainty model is looked for, consisting of a nominal model and an additive dynamic perturbation accounting for the modeling errors. The nominal model is chosen within a class of linearly parametrized models with transfer function of given (possibly low) order. An estimate of the parameters minimizing the H_∞ modeling error is obtained by minimizing an upper bound of the worst case (with respect to modeling error) second moment of the estimation error. Then, a bound in the frequency domain guaranteeing to include, with probability α, the frequency response error between the estimated nominal model and the unknown system is derived