In this paper, we extendthe structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model reduction bases to satisfy different types of interpolation conditions. First, we establish the analysis for transfer function interpolation for single-input single-output structured bilinear systems. Then, we extend these results to the case of multi-input multi-output structured bilinear systems by matrix interpolation. The effectiveness of our structure-preserving approach is illustrated by means of various numerical examples.

中文翻译：

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双线性控制系统的保结构插值

在本文中，我们将最初为线性系统开发的保留结构插值模型简化​​框架扩展到结构化双线性控制系统。具体来说，我们给出模型归约基的明确构造公式，以满足不同类型的插值条件。首先，我们建立了单输入单输出结构化双线性系统传递函数插值的分析。然后，通过矩阵插值，将这些结果扩展到多输入多输出结构化双线性系统的情况。通过各种数值示例说明了我们的结构保留方法的有效性。