Fast Positive-Real Balanced Truncation of Symmetric Systems Using Cross Riccati Equations

We present a computationally efficient implementation of positive-real balanced truncation (PRBT) for symmetric multiple-input multiple-output (MIMO) systems. The solution of a pair of algebraic Riccati equations (AREs) in conventional PRBT, whose complexity limits practical large-scale realization, is replaced with the solution of one cross Riccati equation (XRE). The cross-Riccatian solution then permits simple construction of projection matrices without actually balancing the system. The method encompasses passive linear networks, as commonly used in interconnect and package modelings, due to their inherent reciprocity and therefore symmetric transfer functions. Effectiveness of the proposed approach is verified by numerical examples