TY - GEN
T1 - Littlewood-Offord theory and controllability of random structures
AU - O'Rourke, Sean
AU - Touri, Behrouz
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/12/27
Y1 - 2016/12/27
N2 - Motivated by recent developments in random matrix theory through the study of inverse Littlewood-Offord problems, we investigate the controllability of random binary symmetric matrices. We show that, as the dimension of the state space goes to infinity, the probability of (A,b) being controllable approaches one for many choices of the vector b including elements of the standard basis, the all-one vector, and random binary vectors. In particular, we verify a conjecture of Godsil [1] and show that most systems are controllable from single inputs.
AB - Motivated by recent developments in random matrix theory through the study of inverse Littlewood-Offord problems, we investigate the controllability of random binary symmetric matrices. We show that, as the dimension of the state space goes to infinity, the probability of (A,b) being controllable approaches one for many choices of the vector b including elements of the standard basis, the all-one vector, and random binary vectors. In particular, we verify a conjecture of Godsil [1] and show that most systems are controllable from single inputs.
UR - http://www.scopus.com/inward/record.url?scp=85010739048&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2016.7799064
DO - 10.1109/CDC.2016.7799064
M3 - Conference contribution
AN - SCOPUS:85010739048
T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
SP - 5195
EP - 5200
BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 55th IEEE Conference on Decision and Control, CDC 2016
Y2 - 12 December 2016 through 14 December 2016
ER -