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Gramian‐based model order reduction of parameterized time‐delay systems
Author(s) -
Wang Xiang,
Zhang Zheng,
Wang Qing,
Wong Ngai
Publication year - 2014
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.1884
Subject(s) - parameterized complexity , reduction (mathematics) , parametric statistics , computer science , algorithm , truncation (statistics) , control theory (sociology) , mathematics , model order reduction , statistics , machine learning , artificial intelligence , projection (relational algebra) , geometry , control (management)
Time‐delay systems (TDSs) frequently arise in circuit simulation especially in high‐frequency applications. Model order reduction (MOR) techniques can be used to facilitate the simulation of TDSs. On the other hand, many kinds of variations, such as temperature and geometric uncertainties, can have significant impact on the transient responses of TDSs. Therefore, it is important to preserve parametric dependence during the MOR procedure. This paper presents a new parameterized MOR scheme for TDSs with parameter variations. We derive parameterized reduced‐order models (ROMs) for TDSs using balanced truncation by approximating the Gramians in the multi‐dimensional space of parameters. The resulting ROMs can preserve the parametric dependence, making it efficient for repeated simulations under different parameter settings. Numerical examples are presented to verify the accuracy and efficiency of our proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.