@inproceedings{128a4c159bd74abdadb4f54a1fcea5f7,

title = "Anisotropic norm Bounded Real Lemma for linear discrete time varying systems",

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.",

keywords = "Anisotropic norm, Bounded Real Lemma, Difference riccati equation, Stochastic robust control",

author = "Maximov, {Eugene A.} and Kurdyukov, {Alexander P.} and Vladimirov, {Igor G.}",

year = "2011",

doi = "10.3182/20110828-6-IT-1002.00075",

language = "English",

isbn = "9783902661937",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "IFAC Secretariat",

number = "1 PART 1",

pages = "4701--4706",

booktitle = "Proceedings of the 18th IFAC World Congress",

edition = "1 PART 1",

}