Identification in H∞: linear algorithms

In this paper a series of system identificaion techniques are developed which are compatible with current robust controller design methodologies. These techniques are applicable to a broad class of stable, distributed, linear, shift-invariant systems. The information necessary for their application consists of a priori estimates on the relative stability and "steady state gain" of the unknown system together with a finite number of possibly corrupt frequency response samples. Given this information the algorithms established yield both identified models and explicit H_∞ norm error bounds. These algorithms are developed as extensions of a recently proposed polynomial interpolation approach to H_∞ identification which is shown here to diverge in the face of corrupted data. The fact that these algorithms are linear functions of the frequency response data and depend explicitly on the a priori information are singled out as characteristics which distinguish them from other algorithms recently established by the authors.