Cross-Gramian-Based Model Reduction for Descriptor Systems
Abstract
:1. Introduction
2. Model Reduction Based on Gramians
2.1. Preliminaries
- (a)
- the descriptor system is completely controllable;
- (b)
- for all and ;
- (c)
- for all and ;
- (d)
- and .
- (a)
- the descriptor system is completely observable;
- (b)
- for all and ;
- (c)
- for all and ;
- (d)
- and .
- the proper Hankel singular values are defined as the square roots of the largest eigenvalues of .
- the improper Hankel singular values are defined as the square roots of the largest eigenvalues of .
2.2. Model Reduction Based on Gramians for Descriptor Systems
Algorithm 1The BFSR method based on Gramians |
|
Algorithm 2LR-ADI for PGCTLE |
|
Algorithm 3LR-Smith for PGDTLE |
|
3. Model Reduction Based on Cross Gramians
3.1. Cross-Gramian-Based Balanced Realization
3.2. Cross-Gramian-Based Model Reduction
Algorithm 4The BFSR method based on cross Gramians |
|
3.3. Low-Rank Iterative Methods for PGCTSE and PGDTSE
Algorithm 5LR-ADI for PGCTSE |
|
Algorithm 6LR-Smith for PGDTSE |
|
4. Numerical Experiments
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Lin, Y. Cross-Gramian-Based Model Reduction for Descriptor Systems. Symmetry 2022, 14, 2400. https://doi.org/10.3390/sym14112400
Lin Y. Cross-Gramian-Based Model Reduction for Descriptor Systems. Symmetry. 2022; 14(11):2400. https://doi.org/10.3390/sym14112400
Chicago/Turabian StyleLin, Yiqin. 2022. "Cross-Gramian-Based Model Reduction for Descriptor Systems" Symmetry 14, no. 11: 2400. https://doi.org/10.3390/sym14112400
APA StyleLin, Y. (2022). Cross-Gramian-Based Model Reduction for Descriptor Systems. Symmetry, 14(11), 2400. https://doi.org/10.3390/sym14112400