{"title":"Solution of the Spectrum Allocation Problem for a Linear Control System with Closed Feedback","authors":"S. P. Zubova, E. V. Raetskaya","doi":"10.1134/s0012266124060065","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A method for constructing a feedback matrix to solve the spectrum allocation (spectrum\ncontrol; pole assignment) problem for a linear dynamical system is given. A new proof of the\nwell-known theorem about the connection between the complete controllability of a dynamical\nsystem and the existence of a feedback matrix is formed in the process of constructing the cascade\ndecomposition method. The entire set of arbitrary elements affecting the nonuniqueness of the\nmatrix is identified. Examples of constructing a feedback matrix in the case of a real spectrum\nand in the presence of complex conjugate eigenvalues as well as for the case of multiple eigenvalues\nare given. The stability of the specified spectrum under small perturbations of system parameters\nwith a fixed feedback matrix is studied.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-19","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/s0012266124060065","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
A method for constructing a feedback matrix to solve the spectrum allocation (spectrum
control; pole assignment) problem for a linear dynamical system is given. A new proof of the
well-known theorem about the connection between the complete controllability of a dynamical
system and the existence of a feedback matrix is formed in the process of constructing the cascade
decomposition method. The entire set of arbitrary elements affecting the nonuniqueness of the
matrix is identified. Examples of constructing a feedback matrix in the case of a real spectrum
and in the presence of complex conjugate eigenvalues as well as for the case of multiple eigenvalues
are given. The stability of the specified spectrum under small perturbations of system parameters
with a fixed feedback matrix is studied.
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