{"title":"Spectrum Assignment for a System of Neutral Type","authors":"A. V. Metel’skii","doi":"10.1134/s0012266124010099","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For a linear autonomous system of neutral type with commensurable delays, an algorithm\nis given for solving the modal controllability problem (in particular, the finite spectrum\nassignment problem), which provides a closed-loop system with a given characteristic\nquasipolynomial. A procedure for editing the finite part of the spectrum is proposed. A criterion\nfor exponential stabilization of the system under study is constructively justified. When the\ncriterion is met, the closed-loop system can be made exponentially stable according to the\nproposed spectral reduction algorithm. The obtained statements and spectrum assignment\nalgorithms are illustrated with examples.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","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/s0012266124010099","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
For a linear autonomous system of neutral type with commensurable delays, an algorithm
is given for solving the modal controllability problem (in particular, the finite spectrum
assignment problem), which provides a closed-loop system with a given characteristic
quasipolynomial. A procedure for editing the finite part of the spectrum is proposed. A criterion
for exponential stabilization of the system under study is constructively justified. When the
criterion is met, the closed-loop system can be made exponentially stable according to the
proposed spectral reduction algorithm. The obtained statements and spectrum assignment
algorithms are illustrated with examples.
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