On partial-fraction expansion based frequency weighted balanced truncation

In this paper, we present some remarks on frequency weighted balanced truncation technique based on partial-fraction-expansion idea. In particular we show that two frequency weighted balanced truncation techniques [4], [11] based on partial-fraction-expansion idea are special cases of a more general technique introduced recently in [10]

[1]  D. Enns Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[2]  B. Anderson,et al.  Frequency-weighted optimal Hankel-norm approximation of stable transfer functions , 1985 .

[3]  B. Anderson,et al.  Frequency weighted balanced reduction technique: a generalization and an error bound , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[4]  Ching-An Lin,et al.  Model Reduction via Frequency Weighted Balanced Realization , 1990, 1990 American Control Conference.

[5]  Jing Wang,et al.  Frequency-Weighted Model Reduction Method with Error Bounds for 2-D Separable Denominator Discrete Systems , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[6]  Victor Sreeram,et al.  Partial-Fraction Expansion Based Frequency Weighted Model Reduction Technique With Error Bounds , 2007, IEEE Transactions on Automatic Control.

[7]  V. Sreeram,et al.  A new frequency-weighted balanced truncation method and an error bound , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[8]  K. Zhou Frequency-weighted L_∞ nomn and optimal Hankel norm model reduction , 1995 .

[9]  Gene F. Franklin,et al.  Model reduction via balanced realizations: an extension and frequency weighting techniques , 1988 .

[10]  A. G. Madievski,et al.  New results on frequency weighted balanced reduction technique , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[11]  Victor Sreeram,et al.  New results on partial fraction expansion based frequency weighted balanced truncation , 2009, 2009 American Control Conference.

[12]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[13]  B. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .