On robust control synthesis and analysis in a Hilbert space

The motivation for this paper stems from the need to develop a uniform fram ework for addressing problems in identification and robust control. System identification for infinite-dimensional Hilbert spaces has been addressed e arlier by the authors. System identification set in an Hilbert space result s in uncertain models where the description of non-parametric error is typi cally a ball belonging to the Hilbert space. The scope of this paper is to complement these results - develop robust control-synthesis and analysis re sults - for some special, yet, important cases. In this paper we derive a c onvex parameterization of robustly stabilizing controllers for LTI discrete -time systems defined on Hilbert spaces. The perturbations are of rank-one type having both real-parametric and non-parametric components. The paramet erization allows for imposing other constraints to obtain meaningful perfor mance from the controller. Analysis tools are also developed for robust sta bility under SISO block-diagonally structured perturbations. The robustness analysis problem reduces to a finite-dimensional LMI verification which ma kes the procedure extremely efficient. (C) 2000 Published by Elsevier Scien ce B.V. All rights reserved.