On Identification for Robust Control

Given measured data we propose a model consisting of a linear, time-invariant system aaected by norm-bounded perturbation. In this paper we examine the special case of (real) parameter uncertainty. The plants belonging to the resulting uncertain family form a convex set. A robust control method based on strict-positive realness results can be applied. This method allows the computation of a controller which maximizes the stability margin. Lower and upper bounds of the optimal stability margin are obtained in terms of diierent measures of the uncertainty. The approach depends on two key parameters: the bound of the perturbation, and the input used to obtain the data. It turns out that the size of the uncertain family can be reduced by intersecting the model families obtained through the use of diierent inputs.