Second-order balanced truncation for passive-order reduction of RLCK circuits

In this paper, we propose a novel model-order reduction (MOR) approach, second-order balanced truncation (BT) for passive-order reduction (SBPOR), which is the first second-order BT method proposed for passive reduction of RLCK circuits. By exploiting the special structure information in the circuit formulation, second-order Gramians are defined based on a symmetric first-order realization in descriptor from. As a result, SBPOR can perform the traditional balancing with passivity-preserving congruency transformation at the cost of solving one generalized Lyapunov equation. Owing to the second-order formulation, SBPOR also preserves the structure information inherent to RLCK circuits. We further propose, second-order Gramian approximation (SOGA) version of SBPOR, to mitigate high computational cost of solving Lyapunov equation. Experimental results demonstrate that SBPOR and SOGA are globally more accurate than the Krylov subspace based approaches.