On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems

Balanced truncation model reduction for linear systems yields reduced-order models that satisfy a well-known error bound in terms of a system's Hankel singular values. This bound is known to hold with equality under certain conditions, such as when the full-order system is state-space symmetric. In this work, we derive more general conditions in which the balanced truncation error bound holds with equality. We show that this holds for single-input, single-output systems that exhibit a generalized type of state-space symmetry based on the sign parameters corresponding to a system's Hankel singular values. We prove an additional result that shows how to determine this state-space symmetry from the arrowhead realization of a system, if available. In particular, we provide a formula for the sign parameters of an arrowhead system in terms of the off-diagonal entries of its arrowhead realization. We then illustrate these results with an example of an arrowhead system arising naturally in power systems modeling that motivated our study.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2022

Author dc:creator

• Reiter, Sean Joseph

Chair dc:contributor.committeechair

• Embree, Mark P.

Committee members dc:contributor.committeemember

• Beattie, Christopher A.
• Gugercin, Serkan
• Kekatos, Vasileios

• Model Reduction
• Balanced Truncation
• Error Bound
• Arrowhead Systems
• Power Systems

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:33886

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/107999