{"title":"Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises","authors":"A. V. Yurchenkov, I. R. Belov","doi":"10.1134/s00122661230110101","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a discrete-time-invariant system with multiplicative noise with\nimplementation in the state space. The exogenous disturbance is chosen from the class of\ntime-invariant ergodic sequences of nonzero colorness. We consider the level of mean anisotropy of\nthe exogenous disturbance to be bounded by a known value. Conditions for the anisotropic norm\nto be bounded by a given number are obtained in terms of solving a matrix system of inequalities\nwith a convex constraint of a special type. It is demonstrated how, on the basis of the obtained\nconditions, to construct a static state control that ensures the minimum value of the anisotropic\nnorm of the system enclosed by this control.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s00122661230110101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a discrete-time-invariant system with multiplicative noise with
implementation in the state space. The exogenous disturbance is chosen from the class of
time-invariant ergodic sequences of nonzero colorness. We consider the level of mean anisotropy of
the exogenous disturbance to be bounded by a known value. Conditions for the anisotropic norm
to be bounded by a given number are obtained in terms of solving a matrix system of inequalities
with a convex constraint of a special type. It is demonstrated how, on the basis of the obtained
conditions, to construct a static state control that ensures the minimum value of the anisotropic
norm of the system enclosed by this control.
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