Identification in H∞: a robustly convergent, nonlinear algorithm

Abstract

In this paper a system identification technique is developed which is compatible with current robust controller design methodologies. This technique is applicable to a broad class of stable, distributed, linear, shift-invariant systems. The information necessary for the application of this technique 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 estimates. Given this information an algorithm is specified which yields both an identified model and explicit H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm error bounds. Several interesting properties of this algorithm are also discussed. Among them, the fact the algorithm is a nonlinear function of the frequency response data, and that it is robustly convergent with respect to the a priori information on relative stability and gain are singled out as characteristics which distinguish this algorithm from others currently under development by the authors.