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Journal of Control Science and Engineering
Volume 2012 (2012), Article ID 302498, 9 pages
Research Article

Second-Order Model Reduction Based on Gramians

School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, Shandong 250014, China

Received 22 August 2011; Accepted 2 January 2012

Academic Editor: S. Skogestad

Copyright © 2012 Cong Teng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical systems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they are competitive and more favorable for large-scale systems. Numerical examples show the validity of the algorithms. Error bounds on error systems are discussed. Some observations are given on structures of Gramians of second order linear systems.