Abstract: In order to improve the approximation performance over a pre-specified finite frequency interval for the model order reduction problem of linear continuous-time switched systems, this paper develops a parameterized frequency-dependent balanced truncation method. Firstly, the generalized finite-frequency   performance index is introduced to describe the approximation performance over finite-frequency ranges. Then, the finite-frequency performance for both the continuous-time linear switched system and the corresponding parameterized frequency-dependent mapped discrete-time systems is established. Furthermore, the frequency-dependent balanced truncation algorithm is proposed to generate the desired reduced order model. Finally, a numerical example is given to show the effectiveness of the proposed approach.

Key words: Balanced truncation, model order reduction, linear switched systems, finite-frequency range

摘要： 为得到了在针对连续时间线性切换系统模型降阶时更佳的有限频域区间内模型逼近性能，提出一类基于频率参数依赖的平衡截断模型降阶方法。首先引入了一类可近似刻画线性切换系统有限频域下模型逼近性能的广义有限频 指标，并进一步在线性时不变系统相关理论的基础上推导给出了连续时间线性切换系统和其离散时间域下参数化频率依赖映射系统之间的全频/有限频性能之间的关系，最终给出了用于求解降阶切换系统模型的参数化频率依赖平衡截断算法。数值例子表明了所提出方法的有效性。

关键词: 平衡截断, 模型降阶, 线性切换系统, 有限频域