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

2018/11/12 by Yuichi Tanji, Tanji, Yuichi
Engineering · Mathematics · Physics and Astronomy · #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations #Real-time simulation and control systems

paper · pdf · doi:10.48550/arxiv.1811.04630

openalex publication_date 2018/11/12 · openalex created_date 2018/11/16 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Principal component analysis in linear systems: Controllability, observability, and model reduction

Related

• Balancing-based model reduction for switched descriptor systems
• Structure-preserving linear quadratic Gaussian balanced truncation for port-Hamiltonian descriptor systems
• Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems
• A Rosenbrock framework for tangential interpolation of port-Hamiltonian descriptor systems
• Balanced Truncation of Descriptor Systems with a Quadratic Output