Graph spectra and modal dynamics of oscillatory networks

Our research focuses on developing design-oriented analytical tools that enable us to better understand how a network comprising dynamic and static elements behaves when it is set in oscillatory motion, and how the interconnection topology relates to the spectral properties of the system. Such oscillatory networks are ubiquitous, extending from miniature electronic circuits to large-scale power networks. We tap into the rich mathematical literature on graph spectra, and develop theoretical extensions applicable to networks containing nodes that have finite nonnegative weights-including nodes of zero weight, which occur naturally in the context of power networks. We develop new spectral graph-theoretic results spawned by our engineering interests, including generalizations (to node-weighted graphs) of various structure-based eigenvalue bounds. The central results of this thesis concern the phenomenon of dynamic coherency, in which clusters of vertices move in unison relative to each other. Our research exposes the relation between coherency and network structure and parameters. We study both approximate and exact dynamic coherency. Our new understanding of coherency leads to a number of results. We expose a conceptual link between theoretical coherency and the confinement of an oscillatory mode to a node cluster. We show how the eigenvalues of a coherent graph relate to those of its constituent clusters.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2003

Author dc:creator

• Ayazifar, Babak, 1967-

Advisor dc:contributor.advisor

• George C. Verghese.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/16913

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/16913