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Passivity‐preserving model reduction of differential‐algebraic equations in circuit simulation
Author(s) -
Reis Timo,
Stykel Tatjana
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700164
Subject(s) - passivity , differential algebraic equation , reduction (mathematics) , algebraic riccati equation , algebraic number , algebraic equation , mathematics , extension (predicate logic) , riccati equation , model order reduction , differential equation , truncation (statistics) , differential algebraic geometry , reduction of order , differential (mechanical device) , ordinary differential equation , mathematical analysis , computer science , algorithm , physics , nonlinear system , geometry , projection (relational algebra) , statistics , engineering , quantum mechanics , electrical engineering , thermodynamics , programming language
We present an extension of the positive real balanced truncation model reduction method for differential‐algebraic equations that arise in circuit simulation. This method is based on balancing the solutions of the projected generalized algebraic Riccati equations. Important properties of this method are that passivity is preserved in the reduced‐order model and that there exists an approximation error bound. Numerical solution of the projected Riccati equations using the special structure of circuit equations is also discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)