TY - GEN
T1 - On frequency weighted balanced truncation
T2 - 6th European Control Conference, ECC 2001
AU - Van Gestel, Tony
AU - De Moor, Bart
AU - Anderson, Brian D.O.
AU - Van Overschee, Peter
N1 - Publisher Copyright:
© 2001 EUCA.
PY - 2001
Y1 - 2001
N2 - The concept of frequency weighted balancing, as proposed by Enns, is a generalization of internally balanced model truncation. Internally balanced truncation is simple to apply and additionally attractive because of the existence of an upper -ffœ error bound that is a function of the neglected Hankel singular values. A conjecture on the generalization of this upper error bound for the case of frequency weighted balanced truncation was formulated by Enns, but the proof has not been found. In this paper, Enns' conjecture is refuted and it is shown that there does not exist a frequency weighted upper error bound that depends only on neglected frequency weighted Hankel singular values. It is explained that this is due to cross terms which appear in the frequency weighted error bound. However, these cross terms are inherent in the frequency weighted balancing technique proposed by Enns.
AB - The concept of frequency weighted balancing, as proposed by Enns, is a generalization of internally balanced model truncation. Internally balanced truncation is simple to apply and additionally attractive because of the existence of an upper -ffœ error bound that is a function of the neglected Hankel singular values. A conjecture on the generalization of this upper error bound for the case of frequency weighted balanced truncation was formulated by Enns, but the proof has not been found. In this paper, Enns' conjecture is refuted and it is shown that there does not exist a frequency weighted upper error bound that depends only on neglected frequency weighted Hankel singular values. It is explained that this is due to cross terms which appear in the frequency weighted error bound. However, these cross terms are inherent in the frequency weighted balancing technique proposed by Enns.
KW - Balanced truncation
KW - Frequency weighted balancing
KW - Hankel singular values
KW - Linear systems
KW - Model reduction
UR - http://www.scopus.com/inward/record.url?scp=84947474996&partnerID=8YFLogxK
U2 - 10.23919/ecc.2001.7076302
DO - 10.23919/ecc.2001.7076302
M3 - Conference contribution
T3 - 2001 European Control Conference, ECC 2001
SP - 2493
EP - 2498
BT - 2001 European Control Conference, ECC 2001
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 4 September 2001 through 7 September 2001
ER -