期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 66, 期 1, 页码 391-398出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2020.2981425
关键词
Controllability; Voltage control; Color; Knowledge engineering; Symmetric matrices; Linear systems; Network controllability; pattern matrices; strong structural controllability; structured system
资金
- China Scholarship Council
- Data Science and Systems Complexity Center at the Univrsity of Groningen
This article discusses strong structural controllability of linear systems, establishing necessary and sufficient algebraic conditions as well as a graph-theoretic condition for the full rank property of pattern matrices. Introducing a new color change rule, the study provides a comprehensive understanding of strong structural controllability and how it builds upon existing literature.
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.
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