2012/08/20 by Eugene A. Maximov, Maximov, Eugene A., Alexander P. Kurdyukov +3
Engineering · #60G15 #93B05 #93C55 #93E15 #93E20 #94A17 #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Fault Detection and Control Systems #Information Theory (cs.IT) #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1208.4081
openalex publication_date 2012/08/20 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We consider a finite horizon linear discrete time varying system whose input\nis a random noise with an imprecisely known probability law. The statistical\nuncertainty is described by a nonnegative parameter a which constrains the\nanisotropy of the noise as an entropy theoretic measure of deviation of the\nactual noise distribution from Gaussian white noise laws with scalar covariance\nmatrices. The worst-case disturbance attenuation capabilities of the system\nwith respect to the statistically uncertain random inputs are quantified by the\na-anisotropic norm which is an appropriately constrained operator norm of the\nsystem. We establish an anisotropic norm bounded real lemma which provides a\nstate-space criterion for the a-anisotropic norm of the system not to exceed a\ngiven threshold. The criterion is organized as an inequality on the\ndeterminants of matrices associated with a difference Riccati equation and\nextends the Bounded Real Lemma of the H-infinity-control theory. We also\nprovide a necessary background on the anisotropy-based robust performance\nanalysis.\n