A Unifying Framework for Strong Structural Controllability

• 成果类型: Article
• 署名作者: Jia, Jiajia; van Waarde, Henk J.; Trentelman, Harry L.; Camlibel, M. Kanat
• 署名单位: University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2981425
• 发表日期: 2021
• 页码: 391-398
• 关键词: Controllability; Voltage control; color; Knowledge engineering; Symmetric matrices; Linear systems; network controllability; pattern matrices; strong structural controllability; structured system

摘要

This article deals with strong structural controllability of linear systems. In contrast to the existing work, the structured systems studied in this article have a so-called zero/nonzero/arbitrary structure, which means that some of the entries are equal to zero, some of the entries are arbitrary but nonzero, and the remaining entries are arbitrary (zero or nonzero). We formalize this in terms of pattern matrices, whose entries are either fixed zero, arbitrary nonzero, or arbitrary. We establish necessary and sufficient algebraic conditions for strong structural controllability in terms of full rank tests of certain pattern matrices. We also give a necessary and sufficient graph-theoretic condition for the full rank property of a given pattern matrix. This graph-theoretic condition makes use of a new color change rule that is introduced in this article. Based on these two results, we then establish a necessary and sufficient graph-theoretic condition for strong structural controllability. Moreover, we relate our results to those that exist in the literature and explain how our results generalize previous work.