Model order reduction methods via high-order Krylov subspace for bilinear time-delay systems are developed in this paper. The proposed methods are based on the expansion of the Taylor series or Laguerre series. The obtained reduced systems can not only match certain expansion coefficients but also preserve the structure of the original system. We also briefly discuss the two-sided projection reduction method. To address the implementation of our approach, we utilize the high-order block Arnoldi algorithm to generate projection matrices and employ the genetic algorithm to optimize parameter selection during the reduction process. Finally, we validate the performance of the proposed reduction methods through numerical results.

中文翻译：

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双线性时滞系统的高阶Krylov子空间模型降阶方法

本文开发了双线性时滞系统的通过高阶 Krylov 子空间的模型降阶方法。所提出的方法基于泰勒级数或拉盖尔级数的展开。得到的简化系统不仅可以匹配一定的展开系数，而且可以保留原系统的结构。我们还简要讨论了两侧投影缩减方法。为了解决我们的方法的实现，我们利用高阶块 Arnoldi 算法来生成投影矩阵，并利用遗传算法来优化缩减过程中的参数选择。最后，我们通过数值结果验证了所提出的缩减方法的性能。