Nearly optimal model sets in H∞ identification

H_∞ identification of model sets for LTI discrete-time exponentially stable SISO systems, from noise corrupted measurements in the time and/or the frequency domain, is considered. The assumptions on the noise can account for information on its maximal magnitude and deterministic uncorrelation properties. Identification of optimal model sets requires the computation of the Chebicheff center in a weighted H_∞ norm of the unfalsified systems set. Such a problem is NP-hard and alternative algorithms have been investigated, simpler to use, at the expense of identification accuracy degradation. This is measured by the suboptimality level of the identified model set, i.e. the ratio between the achieved identification error and the minimal one. A new interpolatory algorithm is here presented, able to identify, with manageable computational complexity, model sets having suboptimality level guaranteed to be less than √2 and typically quite close to 1. By suitably approximating this "nearly optimal" model set, tight reduced order model sets are derived, whose order may be selected by suitably trading between model set complexity and achievable suboptimality level.