{"title":"二阶线性系统可达区域大小的变化","authors":"D. I. Bugrov, M. I. Bugrova","doi":"10.3103/S0027133022020029","DOIUrl":null,"url":null,"abstract":"<p>A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on the phase plane. A monotonic dependence of the size of the reachable region on the parameters of the system is shown.</p>","PeriodicalId":710,"journal":{"name":"Moscow University Mechanics Bulletin","volume":"77 2","pages":"47 - 52"},"PeriodicalIF":0.3000,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Variation of the Size of Reachable Region of Second-Order Linear System\",\"authors\":\"D. I. Bugrov, M. I. Bugrova\",\"doi\":\"10.3103/S0027133022020029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on the phase plane. A monotonic dependence of the size of the reachable region on the parameters of the system is shown.</p>\",\"PeriodicalId\":710,\"journal\":{\"name\":\"Moscow University Mechanics Bulletin\",\"volume\":\"77 2\",\"pages\":\"47 - 52\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2022-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Moscow University Mechanics Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.3103/S0027133022020029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mechanics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.3103/S0027133022020029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
Variation of the Size of Reachable Region of Second-Order Linear System
A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on the phase plane. A monotonic dependence of the size of the reachable region on the parameters of the system is shown.
期刊介绍：
Moscow University Mechanics Bulletin is the journal of scientific publications, reflecting the most important areas of mechanics at Lomonosov Moscow State University. The journal is dedicated to research in theoretical mechanics, applied mechanics and motion control, hydrodynamics, aeromechanics, gas and wave dynamics, theory of elasticity, theory of elasticity and mechanics of composites.
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