TY - JOUR
T1 - A Unifying Framework for Strong Structural Controllability
AU - Jia, Jiajia
AU - Van Waarde, Henk J.
AU - Trentelman, Harry L.
AU - Camlibel, M. Kanat
N1 - Funding Information:
Manuscript received September 2, 2019; revised January 13, 2020; accepted February 29, 2020. Date of publication March 17, 2020; date of current version December 24, 2020. The work of Jiajia Jia was supported by the China Scholarship Council. The work of Henk J. van Waarde was supported by the Data Science and Systems Complexity Center at the Univrsity of Groningen. Recommended by Associate Editor Z. Gao. (Corresponding author: M. Kanat Camlibel.) The authors are with the Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen 9747 AG, Groningen, The Netherlands (e-mail: [email protected]; h.j.van.waarde@ rug.nl; [email protected]; [email protected]). Digital Object Identifier 10.1109/TAC.2020.2981425
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/1
Y1 - 2021/1
N2 - 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.
AB - 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.
KW - Network controllability
KW - pattern matrices
KW - strong structural controllability
KW - structured system
UR - http://www.scopus.com/inward/record.url?scp=85094425162&partnerID=8YFLogxK
U2 - 10.1109/TAC.2020.2981425
DO - 10.1109/TAC.2020.2981425
M3 - Article
AN - SCOPUS:85094425162
SN - 0018-9286
VL - 66
SP - 391
EP - 398
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 1
M1 - 9039736
ER -