Mixed Riccati–Lyapunov Balanced Truncation for Order Reduction of Electrical Circuit Systems

This paper proposes a novel algorithm, termed Mixed Riccati–Lyapunov Balanced Truncation (MRLBT), tailored for order reduction of Linear Time-Invariant Continuous-Time Descriptor Systems (LTI-CTD), commonly encountered in electrical and electronic circuit modeling. The MRLBT approach synergistically combines the advantages of balanced truncation (BT) and positive-real balanced truncation (PRBT) techniques while mitigating their limitations. Unlike BT, which preserves stability but not passivity, and PRBT, which retains passivity at the expense of larger reduction errors, MRLBT ensures the preservation of both stability and passivity inherent in the original system. Additionally, MRLBT achieves reduced computational complexity and minimized order reduction errors compared to PRBT. The proposed algorithm transforms the system into an equivalent Mixed Riccati–Lyapunov Balanced form, enabling the construction of a reduced-order model that retains the critical physical properties. Theoretical analysis and proofs are provided, establishing an upper bound on the global order reduction error. The efficacy of MRLBT is demonstrated through a numerical example involving an RLC ladder network, showcasing its superior performance over BT and PRBT in terms of reduced errors in the time and frequency domains.