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A Survey of Model Reduction by Balanced Truncation and Some New Results
Abstract
Balanced truncation is one of the most common model reduction schemes. In this note, we present a survey of balancing related model reduction methods and their corresponding error norms, and also introduce some new results. Five balancing methods are studied: (1) Lyapunov balancing, (2) stochastic balancing, (3) bounded real balancing, (4) positive real balancing and (5) frequency weighted balancing. For positive real balancing, we introduce a multiplicative-type error bound. Moreover, for a certain subclass of positive real systems, a modified positive-real balancing scheme with an absolute error bound is proposed. We also develop a new frequency-weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians. Two numerical examples are illustrated to verify the efficiency of the proposed methods.
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Cited by
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
Benner, P., Gugercin, S., & Willcox, K. (2015) · SIAM Review · doi:10.1137/130932715 · Cited by 1,916
Self-citationPerspective: Sloppiness and emergent theories in physics, biology, and beyond
Transtrum, M. K., Machta, B. B., Brown, K. S., Daniels, B. C., Myers, C. R., & Sethna, J. P. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4923066 · Cited by 311
Zhou, Z., Oguz, O. S., Leibold, M., & Buss, M. (2020) · IEEE Transactions on Robotics · doi:10.1109/tro.2020.2992981 · Cited by 18
Metadata
- Authors
- Gugercin, S., & Antoulas, A. C.
- Venue
- International Journal of Control
- Publisher
- Informa UK Limited
- Published
- 2004-05-20
- Volume
- 77
- Issue
- 8
- Pages
- 748-766
- ISSN
- 0020-7179 (ISSN-L)
- 1366-5820
- OpenAlex
- W2088872157
- Cited by
- 831
- References
- 16
- FWCI
- 37.82
- Type
- journal article
- Language
- en
- Open access
- closed
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