Reciprocal and Positive Real Balanced Truncations for Model Order Reduction of Descriptor Systems

Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two approaches based on standard and generalized algebraic Riccati equations are proposed. To accelerate the algorithms, a fast Riccati solver, RADI (alternating directions implicit [ADI]-type iteration for Riccati equations), is also introduced. As a result, the proposed methods are general and efficient as a model order reduction algorithm for descriptor systems associated with electrical circuit networks.