This paper introduces a model order reduction method that takes advantage of the near orthogonality of lightly damped modes in a system and the modal separation of diagonalized models to reduce the model order of flexible systems in both continuous and discrete time. The reduction method is computationally fast and cheap, not requiring any singular value decompositions or large matrix operations. Numeric solutions to the infinite time Lyapunov equations are presented, and used to solve for the observability and controllability grammians of diagonalized models. Four different modal importance calculations are produced from the diagonalized model's grammians and are compared to the Hankel singular values of balanced model order reduction. The frequency response functions (FRF) of the reduced diagonalized models are compared to models reduced using the balanced reduction method. A weighted integral of the FRF error is taken as a metric for judging which reduction method is better for each individual model. For low order or lightly damped higher order systems the diagonal reduction method results in significantly less FRF error than the balanced model order reduction.

Library of Congress Subject Headings

Engineering mathematics; Electrical engineering--Data processing; Frequency response (Electrical engineering); Matrices; Lyapunov functions

Publication Date


Document Type


Student Type


Degree Name

Electrical Engineering (MS)

Department, Program, or Center

Electrical Engineering (KGCOE)


Mark Hopkins

Advisor/Committee Member

Athimoottil Mathew

Advisor/Committee Member

Vincent Amuso


Physical copy available from RIT's Wallace Library at TA347.D4 C37 2012


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