On Frequency Weighted Balanced Truncation: Hankel Singular Values and Error bounds

摘要

The concept of frequency weighted balancing proposed by Enns is a generalisation of internally balanced model trunctation which is simple to apply and additionally attractive because of the existence of an upper H_∞ error bound that is a function of the neglected Hankel singular values. However, a generalisation of this error bound based on the frequency weighted Hankel singular values has not been reported. I this paper, it is shown that there does not exist a frequency weighted upper error bound that depends only on the neglected frequency weighted Hankel singular values.