Balanced truncation of linear time-invariant systems over finite-frequency ranges

Abstract

AbstractThis paper discusses model order reduction of linear time-invariant (LTI) systems over limited frequency intervals within the framework of balanced truncation. Two new frequency-dependent balanced truncation methods are developed, one is single-frequency (SF)-type frequency-dependent balanced truncation to cope with the cases that only a single dominating point of the operating frequency interval is pre-known, and the other is interval-type frequency-dependent balanced truncation to deal with the case that both the upper and lower bounds of the relevant frequency interval are known a priori. Error bounds for both approaches are derived to estimate the approximation error over a pre-specified frequency interval. In contrast to other error bounds for frequency-weighted or frequency-limited balanced truncation, these bounds are given specifically for the interval under consideration and are thus often sharper than the global bounds for previous methods. We show that the new methods generally lead to good in-band approximation performance, and at the same time provide accurate error bounds under certain conditions. Examples are included for illustration.