Approximate and Exact Controllability of Switched Infinite-Dimensional Linear Systems

• 成果类型: Article
• 署名作者: Guan, Yacun; Yang, Hao; Jiang, Bin
• 署名单位: Nanjing University of Aeronautics & Astronautics
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3121342
• 发表日期: 2022
• 页码: 5304-5317
• 关键词: Controllability; switches; control systems; Linear systems; Aerospace electronics; Hilbert space; Technological innovation; Approximate and exact controllability; controllability Gramian operator; switched infinite-dimensional linear systems (IDLSs)

摘要

This article addresses the approximate and exact controllability issues of switched infinite-dimensional linear systems. First, a controllability map that is related to switching sequence and a controllability Gramian operator are proposed, based on which two necessary and sufficient conditions are established for approximate and exact controllability, respectively. Second, it shows that the obtained conditions can degenerate into the existing controllability criteria of infinite-dimensional linear systems, switched finite-dimensional linear systems, and a single finite-dimensional linear system. Finally, the new results are applied to analyze the approximate controllability of switched linear parabolic systems and the exact controllability of switched linear wave systems. Two examples are given to illustrate the effectiveness of the proposed approaches.