High-order Krylov subspace model order reduction methods for bilinear time-delay systems

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.