{"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":50580,"journal":{"name":"Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124010099","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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