{"title":"Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems","authors":"Yuan Zhang;Yuanqing Xia;Aming Li","doi":"10.1109/TAC.2024.3482100","DOIUrl":null,"url":null,"abstract":"In this article, we explore the structural controllability of switched linear continuous-time systems. We first identify a gap in the proof of a fundamental criterion for the structural controllability of these systems. To solve this problem, we develop several novel graph-theoretic concepts, such as multilayer dynamic graphs, generalized stems/buds, and generalized cacti. Using these concepts, we provide a comprehensive proof for the criterion. Our approach also induces a new, generalized cactus-based graph-theoretic criterion for the structural controllability. This not only extends Lin's cactus-based graph-theoretic condition to switched systems for the first time, but also provides a lower bound for the generic dimension of controllable subspaces of switched systems.","PeriodicalId":13201,"journal":{"name":"IEEE Transactions on Automatic Control","volume":"70 3","pages":"1996-2003"},"PeriodicalIF":7.0000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Transactions on Automatic Control","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/10720174/","RegionNum":1,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we explore the structural controllability of switched linear continuous-time systems. We first identify a gap in the proof of a fundamental criterion for the structural controllability of these systems. To solve this problem, we develop several novel graph-theoretic concepts, such as multilayer dynamic graphs, generalized stems/buds, and generalized cacti. Using these concepts, we provide a comprehensive proof for the criterion. Our approach also induces a new, generalized cactus-based graph-theoretic criterion for the structural controllability. This not only extends Lin's cactus-based graph-theoretic condition to switched systems for the first time, but also provides a lower bound for the generic dimension of controllable subspaces of switched systems.
期刊介绍：
In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering. Two types of contributions are regularly considered:
1) Papers: Presentation of significant research, development, or application of control concepts.
2) Technical Notes and Correspondence: Brief technical notes, comments on published areas or established control topics, corrections to papers and notes published in the Transactions.
In addition, special papers (tutorials, surveys, and perspectives on the theory and applications of control systems topics) are solicited.
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