A new frequency weighted Fourier-based method for model order reduction

Automatica

Volumn 88, Issue , 2018, Pages 107-112

  Rydel, Marek ^a   Stanisławski, Rafał ^a  

^a OPOLE UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Discrete Fourier transform; Frequency weighted; Gramians; Identification and model reduction; Large scale complex systems

Indexed keywords

DIGITAL CONTROL SYSTEMS; DISCRETE FOURIER TRANSFORMS; DISCRETE TIME CONTROL SYSTEMS; LARGE SCALE SYSTEMS; SCALES (WEIGHING INSTRUMENTS); STATE SPACE METHODS;

CONTROLLABILITY AND OBSERVABILITIES; DISCRETE - TIME SYSTEMS; FREQUENCY WEIGHTED; GRAMIANS; HIGH-ORDER STATE SPACE MODELS; LARGE-SCALE COMPLEX SYSTEMS; MODEL ORDER REDUCTION; MODEL REDUCTION;

CONTINUOUS TIME SYSTEMS;

EID: 85038214842     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2017.11.016     Document Type: Article

References (19)

1. Antoulas, A., Approximation of large-scale dynamical system, 2005, Society for Industrial and Applied Mathematics, Philadelphia.
2. Campbell, K., Sreeram, V., & Wang, G. (2000). A frequency-weighted discrete system balanced truncation method and an error bound. In Proc. of the American control conference., Vol. 4 (pp. 2403–2404).
3. Enns, D. (1984). Model reduction with balanced realizations: An error bound and frequency weighted generalization. In 23rd IEEE conference on decision and control (pp. 127–132).
4. Ghafoor, A., Sreeram, V., Partial-fraction expansion based frequency weighted model reduction technique with error bounds. IEEE Transactions on Automatic Control 52:10 (2007), 1942–1948.
5. Imran, M., Ghafoor, A., Sreeram, V., A frequency weighted model order reduction technique and error bounds. Automatica 50:12 (2014), 3304–3309.
6. Imran, M., Ghafoor, A., Sreeram, V., Frequency weighted model order reduction technique and error bounds for discrete time systems. Mathematical Problems in Engineering, 2014, 2014.
7. Lin, C., Chiu, T., Model reduction via frequency weighted balanced realization. Theory and Advanced Technology 8 (1992), 341–451.
8. Moore, B., Principal component analysis in linear systems: Controllability, observability and model reduction. IEEE Transactions on Automatic Control AC–26:1 (1981), 17–32.
9. Penzl, T., Algorithms for model reduction of large dynamical systems. Linear Algebra and its Applications 415 (2006), 322–343.
10. Rydel, M., & Stanisławski, W. (2015). Selection of the objective function of reduction parameter optimization algorithm, and its impact on the properties of reduced MIMO models. In Int. Conf. on methods and models in automation and robotics (pp. 591–595).
11. Sahlan, S., & Sreeram, V. (2009). New results on partial fraction expansion based frequency weighted balanced truncation. In American control conference (pp. 5695–5700).
12. Sreeram, V., Anderson, B. D. O., & Madievski, A. G. (1995). New results on frequency weighted balanced reduction technique. In American control conference (pp. 4004–4009).
13. Sreeram, V., Sahlan, S., Improved results on frequency-weighted balanced truncation and error bounds. International Journal of Robust and Nonlinear 22:11 (2012), 1195–1211.
14. Stanisławski, R., Rydel, M., Latawiec, K.J., Modeling of discrete-time fractional-order state space systems using the balanced truncation method. Journal of the Franklin Institute 354:7 (2017), 3008–3020.
15. Varga, A. (1991). Balancing-free square-root algorithm for computing singular perturbation approximations. In 30th IEEE conference on decision and control,Vol. 2 (pp. 1062–1065).
16. Varga, A., Anderson, B., Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction. Automatica 39:5 (2003), 919–927.
17. Wan Muda, W. M., Sreeram, V., & Iu, H. H. C. (2011). An improved algorithm for partial fraction expansion based frequency weighted balanced truncation. In Proc. of the American control conference (pp. 5037–5042).
18. Wang, G., Sreeram, V., Liu, W.Q., A new frequency-weighted balanced truncation method and an error bound. IEEE Transactions on Automatic Control 44:9 (1999), 1734–1737.
19. Willcox, K., Megretski, A., Fourier series for accurate, stable, reduced-order models in large-scale linear applications. SIAM Journal on Scientific Computing 26:3 (2005), 944–962.