Near aggregation: a time and frequency domain analysis using state trajectories and transfer function residues

In this thesis we investigate concepts associated with aggregation. The basic idea of aggregation is that there exists a reduced order model such that, for an appropriate initial condition, the trajectories of the reduced-order model are linear combinations of the trajectories of the ful 1-order model. We study systems which do not aggregate exactly, but which "nearly aggregate". It is shown that for "nearly aggregable" systems there exists a reduced-order model such that, for an appropriate initial condition, the trajectories of the reduced-order model are near a linear combination of the trajectories of the full-order model. Under certain conditions it has also been shown that near-aggregation is equivalent to near-unobservability (roughly, an invariant subspace close to the null space of C). Here we establish a relationship between near-unobservability and modal measures of observability as suggested by Selective Modal Analysis. With this result we then obtain an upper bound on the norm of the transfer function residue using near-unobservability measures. The Generalized Hessenberg Representation (GHR) and Dual GHR are examined throughout this analysis. It is finally shown that for SISO systems, the residue norm may be expressed in terms of certain parameters of the Dual GHR.

Name thesis:degree_name

M.S.

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Electrical Engineering

Department dc:contributor.department

Electrical Engineering

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1987

Author dc:creator

• Babendreier, Justin Eric

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/91080

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/91080