Worst-case l1 system identification using perturbed ARMA models

Worst case l₁ identification is aimed at identifying a system within a given class, using input-output measurements corrupted by l_∞-bounded noise, and measuring the estimation error according to the l₁ -norm of the impulse response in the worst case, with respect to allowable systems and noise. The properties of nonparametric identification methods have been investigated. With such an approach, the number of measurements needed to estimate n impulse response samples, within a given level of accuracy, grows exponentially with n, leading in most cases to unacceptable experimental conditions. It is shown that significant improvement can be obtained with respect to the nonparametric approach by using more parsimonious classes of models, constituted of mixed parametric and nonparametric models. It is shown how to compute the diameter of information (a typical measure of estimation error in the worst case setting), when the parametric part is linear in the parameters