Robustness analysis tools for an uncertainty set obtained by prediction error identi"cation

This paper presents a robust stability and performance analysis for an uncertainty set delivered by classical prediction error identi"cation. This nonstandard uncertainty set, which is a set of parametrized transfer functions with a parameter vector in an ellipsoid, contains the true system at a certain probability level. Our robust stability result is a necessary and su$cient condition for the stabilization, by a given controller, of all systems in such uncertainty set. The main new technical contribution of this paper is our robust performance result: we show that the worst case performance achieved over all systems in such an uncertainty region is the solution of a convex optimization problem involving linear matrix inequality constraints. Note that we only consider single input}single output systems. 2001 Elsevier Science Ltd. All rights reserved.