Structure-Preserving Model Order Reduction of second-order systems using Iterative Rational Krylov Algorithm

In this work, we are going to discuss the Structure-Preserving Model Order Reduction (SPMOR) techniques of second-order linear time-invariant (LTI) continuous-time systems using the Iterative Rational Krylov Algorithm (IRKA). IRKA is well established for the first-order standard and/or generalized systems. Recently, the idea of this model reduction technique is generalized for second-order systems by converting the system into a first-order form. In this case, one can’t return back to the original second-order system since the structure of the system is already demolished. Sometimes preservation of second-order structure is essential to perform the further simulations of the system. Also, Structure-preserving MOR allows meaningful physical interpretation and provides a more accurate approximation to the full model. We mainly focus on the SPMOR of the second-order systems using IRKA without converting the system into first-order forms. We have applied and numerically investigated the applicability and efficiency of the proposed techniques to some practical data derived from real-world models.