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

  • Authors:

  • X. Bombois;M. Gevers;G. Scorletti;B. D. O. Anderson

  • Affiliations:

  • Section MMR, Department of Applied Physics, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, Netherlands;CESAME, Université Catholique de Louvain, 4 av. G. Lemaitre, 1348 Louvain-la-Neuve, Belgium;LAP ISMRA, 6 boulevard du Maréchal Juin, 14050 Caen Cedex, France;RSISE, The Australian National University, Canberra ACT 0200, Australia

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2001

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Abstract

This paper presents a robust stability and performance analysis for an uncertainty set delivered by classical prediction error identification. 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 sufficient 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.