Anisotropic norm Bounded Real Lemma for linear discrete time varying systems

Eugene A. Maximov, Alexander P. Kurdyukov*, Igor G. Vladimirov

*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy of the noise as an entropy theoretic measure of deviation of the actual noise distribution from Gaussian white noise laws with scalar covariance matrices. The worst-case disturbance attenuation capabilities of the system with respect to the statistically uncertain random inputs are quantified by the a-anisotropic norm which is a constrained operator norm of the system. We establish an anisotropic norm bounded real lemma which provides a state-space criterion for the a-anisotropic norm of the system not to exceed a given threshold. The criterion is organized as an inequality on the determinants of matrices associated with a difference Riccati equation and extends the Bounded Real Lemma of the H-control theory. We also provide a necessary background on the anisotropy-based robust performance analysis.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Pages4701-4706
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
DOIs
Publication statusPublished - 2011
Externally publishedYes

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
Volume44
ISSN (Print)1474-6670

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