SBPOR: Second-Order Balanced Truncation for Passive Order Reduction of RLC Circuits

RLC circuits have been shown to be better formulated as second-order systems instead of first-order systems. The corresponding model order reduction techniques for second- order systems have been developed. However, existing techniques are mainly based on moment-matching concept. While suitable for the reduction of large-scale circuits, those approaches cannot generate reduced models as compact as desired. To achieve smaller models with better error control, a novel technique, SBPOR (Second-order Balanced truncation for Passive Order Reduction), is proposed in this paper, which is the first second-order balanced truncation method proposed for passive reduction of RLC circuits. SBPOR is superior to the pioneering work in the control community because second-order systems can be balanced via congruency transformation without any accuracy loss. In addition, compared with the first-order balanced truncation approaches, SBPOR is a better choice for RLC reduction. SBPOR preserves not only passivity but also the structure information inherent to RLC circuits, which is a special need for RLC reduction. In addition, SBPOR is computationally more efficient as it only needs to solve one linear matrix equation instead of two quadratic matrix equations.