Minimum-Phase Preserving Balanced Truncation with Data-Driven Order Scoring

Abstract

This paper investigates the problem of model-order reduction for linear systems arising from minimum-phase circuits and filters, where stability and frequency characteristics must be preserved. The MPPBT framework uses a Riccati–Lyapunov Gramian pair and constructs a balancing transformation with the sequence of MPPBT singular values, from which a relative error bound in the H∞ norm and a scoring function, Sβ are derived to select the model order. We apply the algorithm to a fourth-order Butterworth low-pass filter with a full-order state dimension, n = 4, and reduced-order models with r = 1, 2, 3 are examined. The results show that the model with r = 3 yields an H∞ error of approximately 6.3 × 10−3 and an H2 error of approximately 2.2 × 10−3. The model with r = 1 gives an H∞ error of approximately 1.46 and an H2 error of approximately 4.8 × 10−1. The model with r = 2 attains a composite score of Sβ ≈ 0.16, preserves stability and the minimum-phase property, and is regarded as a balanced choice between accuracy and complexity. A further comparison on an RLC ladder circuit of order n = 15 shows that at r = 3, MPPBT achieves the lowest H∞ error among BT, PRBT, and MPPBT, while retaining an H2 error close to that of BT.