{"title":"稀疏驱动对称LTI系统可控格律的改进特征值衰减界","authors":"Chenyan Zhu;Sandip Roy","doi":"10.1109/LCSYS.2025.3530636","DOIUrl":null,"url":null,"abstract":"Refined bounds are obtained for the eigenvalues of the controllability Gramian for a linear system with a Hurwitz, symmetric state matrix. The new bounds are phrased in terms of partial condition numbers (ratios of intermediate eigenvalues) of the state matrix. The bounds are found to compare favorably with existing results for several examples, particularly in cases where the system has time-scale separations or multiple eigenvalues in narrow bands.","PeriodicalId":37235,"journal":{"name":"IEEE Control Systems Letters","volume":"8 ","pages":"3362-3367"},"PeriodicalIF":1.9000,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Refined Eigenvalue Decay Bounds for Controllability Gramians of Sparsely-Actuated Symmetric LTI Systems\",\"authors\":\"Chenyan Zhu;Sandip Roy\",\"doi\":\"10.1109/LCSYS.2025.3530636\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Refined bounds are obtained for the eigenvalues of the controllability Gramian for a linear system with a Hurwitz, symmetric state matrix. The new bounds are phrased in terms of partial condition numbers (ratios of intermediate eigenvalues) of the state matrix. The bounds are found to compare favorably with existing results for several examples, particularly in cases where the system has time-scale separations or multiple eigenvalues in narrow bands.\",\"PeriodicalId\":37235,\"journal\":{\"name\":\"IEEE Control Systems Letters\",\"volume\":\"8 \",\"pages\":\"3362-3367\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2025-01-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE Control Systems Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10843789/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Control Systems Letters","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10843789/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Refined Eigenvalue Decay Bounds for Controllability Gramians of Sparsely-Actuated Symmetric LTI Systems
Refined bounds are obtained for the eigenvalues of the controllability Gramian for a linear system with a Hurwitz, symmetric state matrix. The new bounds are phrased in terms of partial condition numbers (ratios of intermediate eigenvalues) of the state matrix. The bounds are found to compare favorably with existing results for several examples, particularly in cases where the system has time-scale separations or multiple eigenvalues in narrow bands.
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