TY - JOUR
T1 - Classification of the structurally controllable zero-patterns for driftless bilinear control systems
AU - Tsopelakos, Aristomenis
AU - Belabbas, Mohamed Ali
AU - Gharesifard, Bahman
N1 - Funding Information:
Manuscript received July 11, 2017; revised November 24, 2017 and April 14, 2018; accepted May 1, 2018. Date of publication May 9, 2018; date of current version March 14, 2019. The work of A. Tsopelakos and M.-A. Belabbas was supported in part by NSF awards EECS 13-07791 and ECCS CAREER 13-51586 and the work of Bahman Gharesifard was supported by the Natural Sciences and Engineering Research Council of Canada. Recommended by Associate Editor L. Xie. (Corresponding Author: Aristomenis Tsopelakos.) A. Tsopelakos and M.-A. Belabbas are with the Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Champaign, IL 61820 USA (e-mail: tsopela2@illinois.edu; belabbas@illinois.edu).
Publisher Copyright:
© 2014 IEEE.
PY - 2019/3
Y1 - 2019/3
N2 - We introduce and study the structural controllability of driftless bilinear control systems. We study two cases: In the first, the system matrices belong to one zero-pattern, and in the second, the system matrices belong to one of several zero-patterns. We refer to them as single and multiple patterns cases. In both cases, we prove that the structural controllability of driftless bilinear control systems is a generic property. We also classify the structurally controllable zero-patterns based on the strong connectivity of their corresponding graph. We provide algorithms that compute the minimum number of matrices needed for the structural controllability of driftless bilinear systems. The results about the structural controllability of driftless bilinear systems can be also used for the study of the structural accessibility of bilinear systems with drift term.
AB - We introduce and study the structural controllability of driftless bilinear control systems. We study two cases: In the first, the system matrices belong to one zero-pattern, and in the second, the system matrices belong to one of several zero-patterns. We refer to them as single and multiple patterns cases. In both cases, we prove that the structural controllability of driftless bilinear control systems is a generic property. We also classify the structurally controllable zero-patterns based on the strong connectivity of their corresponding graph. We provide algorithms that compute the minimum number of matrices needed for the structural controllability of driftless bilinear systems. The results about the structural controllability of driftless bilinear systems can be also used for the study of the structural accessibility of bilinear systems with drift term.
KW - Bilinear systems, strongly connected graphs
KW - structural controllability
KW - transitive Lie algebras
UR - http://www.scopus.com/inward/record.url?scp=85046795322&partnerID=8YFLogxK
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U2 - 10.1109/TCNS.2018.2834822
DO - 10.1109/TCNS.2018.2834822
M3 - Article
AN - SCOPUS:85046795322
SN - 2325-5870
VL - 6
SP - 429
EP - 439
JO - IEEE Transactions on Control of Network Systems
JF - IEEE Transactions on Control of Network Systems
IS - 1
M1 - 8356633
ER -