This 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.

本文讨论了在平衡截断的框架内，线性时不变（LTI）系统在有限频率间隔上的模型阶数减少。开发了两种新的频率相关的平衡截断方法，一种是单频（SF）型频率相关的平衡截断方法，以应对仅知道工作频率间隔的单个控制点的情况，另一种方法是是间隔类型的频率相关的平衡截断处理有关频率间隔的上下限都是先验的情况。推导两种方法的误差范围，以估计预定频率间隔内的近似误差。与频率加权或频率限制的平衡截断的其他误差界限相反，这些界限专门针对所考虑的间隔给出，因此通常比先前方法的全局界限更清晰。我们表明，新方法通常可带来良好的带内逼近性能，同时在某些条件下可提供准确的误差范围。包括示例以供说明。