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Mathematical Problems in Engineering
Volume 2014, Article ID 498453, 8 pages
Research Article

Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

1Military College of Signals, National University of Sciences and Technology (NUST), Islamabad, Pakistan
2School of Electrical, Electronic and Computer Engineering, University of Western Australia, Crawley, WA 6009, Australia

Received 15 December 2013; Revised 10 February 2014; Accepted 11 February 2014; Published 18 March 2014

Academic Editor: Xiaojie Su

Copyright © 2014 Muhammad Imran et al. 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.


Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.