{"title":"确定性系统子空间辨识的非渐近误差分析","authors":"Shuai Sun","doi":"10.1016/j.sysconle.2025.106219","DOIUrl":null,"url":null,"abstract":"<div><div>The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation errors for the system matrices in state-space models and the corresponding system poles, under two unified SIMs, based on a single finite-length input/output sample trajectory. Specifically, we derive non-asymptotic upper bounds on these errors, providing a unified perspective across various SIM variants. Furthermore, we prove that SIMs become ill-conditioned for MIMO systems when the state-to-output dimensionality ratio <span><math><mrow><mi>n</mi><mo>/</mo><mi>m</mi></mrow></math></span> is large, regardless of system parameters. Finally, numerical experiments are conducted to validate the non-asymptotic results and the ill-conditionedness of SIMs.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106219"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-asymptotic error analysis of subspace identification for deterministic systems\",\"authors\":\"Shuai Sun\",\"doi\":\"10.1016/j.sysconle.2025.106219\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation errors for the system matrices in state-space models and the corresponding system poles, under two unified SIMs, based on a single finite-length input/output sample trajectory. Specifically, we derive non-asymptotic upper bounds on these errors, providing a unified perspective across various SIM variants. Furthermore, we prove that SIMs become ill-conditioned for MIMO systems when the state-to-output dimensionality ratio <span><math><mrow><mi>n</mi><mo>/</mo><mi>m</mi></mrow></math></span> is large, regardless of system parameters. Finally, numerical experiments are conducted to validate the non-asymptotic results and the ill-conditionedness of SIMs.</div></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":\"204 \",\"pages\":\"Article 106219\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2025-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems & Control Letters\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167691125002014\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125002014","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Non-asymptotic error analysis of subspace identification for deterministic systems
The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation errors for the system matrices in state-space models and the corresponding system poles, under two unified SIMs, based on a single finite-length input/output sample trajectory. Specifically, we derive non-asymptotic upper bounds on these errors, providing a unified perspective across various SIM variants. Furthermore, we prove that SIMs become ill-conditioned for MIMO systems when the state-to-output dimensionality ratio is large, regardless of system parameters. Finally, numerical experiments are conducted to validate the non-asymptotic results and the ill-conditionedness of SIMs.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.