Aspects of linear estimation in H-infinity

A recent but rapidly maturing held in the area of system identification has been that of 'estimation in H-infinity'. Greatly influencing this work has been the phenomenon that no linear (in-the-data) algorithm exists which is 'robustly convergent'. This paper conducts a study of this issue by combin ing specific new analysis together with existing results from the mathemati cs literature on the topic of polynomial approximation theory. Particular a ttention is paid to the role of model order, and this leads to the consider ation of model order selection from a deterministic worst-case perspective.