Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems

• 成果类型: Article
• 署名作者: Zhang, Yuan; Xia, Yuanqing; Li, Aming
• 署名单位: Beijing Institute of Technology; Peking University; Peking University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3482100
• 发表日期: 2025
• 关键词: STABILIZABILITY; reachability

摘要

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.