BALANCED POSITIVE-REAL TRUNCATION FOR UNSTABLE SYSTEMS: A NOVEL ALGORITHM FOR MODEL REDUCTION IN HIGH-ORDER ELECTRICAL AND ELECTRONIC CIRCUITS

Abstract

This article presents a novel algorithm, named BPRU, designed to reduce the complexity of high-order systems while preserving passive (real-positive) properties and stability. Additionally, this technique can also reduce the order of unstable systems. The approach is grounded in solving real-positive Riccati equations, and Riccati H-Infinity equations, combined with matrix analysis techniques like Cholesky decomposition and Singular Value Decomposition (SVD). These methods transform the system into an energy-balanced state from the control and observation Gramians. MATLAB simulations demonstrate that BPRU maintains the crucial physical properties of electrical and electronic circuits and provides effective model order reduction for systems containing both stable and unstable components. Compared to foundational methods such as Positive Real Balanced truncation (PRR) and H-Infinity Balanced truncation (HBR), BPRU yields significantly lower errors, closely matching the original system's transient and frequency responses. This underscores the efficiency and potential of BPRU in reducing model order for electrical and electronic systems, opening up avenues for research in related applications in this field.