Probability-guaranteed robust H performance analysis

I. Yaesh, S. Boyarski, U. Shaked

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations


This paper addresses the common engineering practice of specifying a required probability of attaining some performance level. The problem setup is that of a standard robust H performance analysis of a parameter-dependent system, except that the parameter hyper-rectangle (box) shrinks in the analysis in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box. An affine-quadratic, multiconvex approach is applied to reduce the overdesign that is inherent in the quadratic approach. A version of the Bounded Real Lemma (BRL) in the form of BiLinear Matrix Inequalities (BLMIs) guarantees a minimum H-norm for a prescribed probability. These BLMIs are solved using an iterative algorithm. A uniform distribution is assumed for the system parameters, according to the uniformity principle. The probability requirement is expressed by a set of LMIs that is derived by extending an existing second-order cone method; these LMIs are to be concurrently solved with the BRL BLMIs. The proposed analysis is demonstrated via a 2-parameter example.

Original languageEnglish
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
EditorsGabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente
PublisherIFAC Secretariat
Number of pages6
ISBN (Print)9783902661746
StatePublished - 2002
Event15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain
Duration: 21 Jul 200226 Jul 2002

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


Conference15th World Congress of the International Federation of Automatic Control, 2002


  • Affine quadratic stability
  • H-infinity optimization
  • Probabilistic performance analysis
  • Robustness


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