Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges

This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new frequency-dependent balanced truncation methods were developed, one is SF-type frequency-dependent balanced truncation to copy with the cases that only a single dominating point of the operating frequency interval is pre-known, the other is interval-type frequencydependent balanced truncation to deal with the cases that both of the upper and lower bound of frequency interval are known a priori. SF-type error bound and interval-type error bound are derived for the first time to estimate the desired approximation error over pre-specified frequency interval. We show that the new methods generally lead to good in-band approximation performance, at the same time, provide accurate error bounds under certain conditions. Examples are included for illustration.