Robustness analysis tools for an uncertainty set obtained by prediction error identification

This paper presents a robust stability and performance analysis for an unce rtainty set delivered by classical prediction error identification. This no nstandard uncertainty set, which is a set of parametrized transfer function s with a parameter vector in an ellipsoid, contains the true system at a ce rtain probability level. Our robust stability result is a necessary and suf ficient condition for the stabilization, by a given controller, of all syst ems in such uncertainty set. The main new technical contribution of this pa per is our robust performance result: we show that the worst case performan ce achieved over all systems in such an uncertainty region is the solution of a convex optimization problem involving linear matrix inequality constra ints. Note that we only consider single input-single output systems. (C) 20 01 Elsevier Science Ltd. All rights reserved.