Least squares methods for H∞ control-oriented system identification

A series of system identification algorithms that yield identified models which are compatible with current robust controller design methodologies is presented. These algorithms are applicable to a broad class of stable, distributed, linear, shift-invariant plants. The a priori information necessary for their application consists of a lower bound on the relative stability of the unknown plant, an upper bound on a certain gain associated with the unknown plant, and an upper bound on the noise level. The a posteriori data information consists of a finite number of corrugated point frequency response estimates of the unknown plant. The extent to which certain standard Hilbert-space or least-squares method are applicable to the H_∞ system identification problem considered is examined. Results are established that connect the H₂ error of the least-squares methods to the H_∞ error needed for control-oriented system identification