{"title":"切换线性系统可控性/可观察性的最小实现","authors":"Yan Zhu , Zhendong Sun","doi":"10.1016/j.nahs.2023.101426","DOIUrl":null,"url":null,"abstract":"<div><p><span>In this work, we address the minimum realization problem for controllability of both continuous-time switched linear systems and reversible discrete-time switched linear systems. For both classes of </span><span><math><mi>n</mi></math></span>-dimensional switched linear systems, we show that <span><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>1</mn></mrow></math></span><span> switches are the tight upper bound for controllability switching realization. The minimum realization problem for observability<span> is also addressed by means of the duality principle.</span></span></p></div>","PeriodicalId":49011,"journal":{"name":"Nonlinear Analysis-Hybrid Systems","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimum realization for controllability/observability of switched linear systems\",\"authors\":\"Yan Zhu , Zhendong Sun\",\"doi\":\"10.1016/j.nahs.2023.101426\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>In this work, we address the minimum realization problem for controllability of both continuous-time switched linear systems and reversible discrete-time switched linear systems. For both classes of </span><span><math><mi>n</mi></math></span>-dimensional switched linear systems, we show that <span><math><mrow><mfrac><mrow><mi>n</mi><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>1</mn></mrow></math></span><span> switches are the tight upper bound for controllability switching realization. The minimum realization problem for observability<span> is also addressed by means of the duality principle.</span></span></p></div>\",\"PeriodicalId\":49011,\"journal\":{\"name\":\"Nonlinear Analysis-Hybrid Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2023-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Hybrid Systems\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1751570X23000973\",\"RegionNum\":2,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Hybrid Systems","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1751570X23000973","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Minimum realization for controllability/observability of switched linear systems
In this work, we address the minimum realization problem for controllability of both continuous-time switched linear systems and reversible discrete-time switched linear systems. For both classes of -dimensional switched linear systems, we show that switches are the tight upper bound for controllability switching realization. The minimum realization problem for observability is also addressed by means of the duality principle.
期刊介绍：
Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.
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