Model reduction via limited frequency interval Gramians

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 55, Issue 9, 2008, Pages 2806-2812

  Ghafoor, Abdul ^a,b   Sreeram, Victor ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

Author keywords

2 D systems; Balanced truncation; Frequency domain Gramians; Frequency weightings; Interval Gramians; Model order reduction

Indexed keywords

DIGITAL CONTROL SYSTEMS; ERROR ANALYSIS; FREQUENCY RESPONSE;

2-D SYSTEMS; BALANCED TRUNCATION; FREQUENCY DOMAIN GRAMIANS; FREQUENCY WEIGHTINGS; INTERVAL GRAMIANS; MODEL ORDER REDUCTION;

DISCRETE TIME CONTROL SYSTEMS;

EID: 56349160286     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.920092     Document Type: Article

References (21)

1. P. K. Aghaee, A. Zilouchian, S. N. Ravesh, and A. H. Zadegan, "Principal of frequency domain balanced structure in linear systems and model reduction," Comput. Elec. Eng., vol. 29, pp. 463-477, 2003.
2. U. M. Al Saggaf and G. F. Franklin, "An error bound for discrete reduced-order model of a linear multivariable system," IEEE Trans. Autom. Control, vol. AC-32, pp. 815-819, 1987.
3. D. F. Enns, "Model reduction with balanced realizations: An error bound and a frequency weighted generalization," in Proc. 23rd IEEE Conf. Decision Contr., 1984, pp. 127-132.
4. W. Gawronski and J.-N. Juang, "Model reduction in limited time and frequency intervals," Int. J. Syst. Sci., vol. 21, no. 2, pp. 349-376, 1990.
5. S. Gugercin and A. C. Antoulas, "A survey of model reduction by balanced truncation and some new results," Int. J. Contr., vol. 77, no. 8, pp. 748-766, 2004.
6. L. G. Horta, J. N. Juang, and R. W. Longman, "Discrete-time model reduction in limited frequency ranges," J. Guid., Contr. Dynam., vol. 16, no. 6, pp. 1125-1130, 1993.
7. L. Lerer and A. C. M. Ran, "A new inertia theorem for Stein equations, inertia of invertible hermitian block Toeplitz matrices and matrix orthogonal polynomials," Integr. Eq. Oper. Theory, vol. 47, pp. 339-360, 2003.
8. B. C. Moore, "Principal component analysis in linear systems: Controllability, observability, and model reduction," IEEE Trans. Autom. Control, vol. AC-26, pp. 17-32, 1981.
9. N. L. Prajapati, D. Chandra, and D. Seshachalam, "Corrections and comments to ls 'Model reduction of discrete linear systems by frequency-domain balanced structure," IEEE Trans. Circuits Syst. I vol. 54, pp. 682-683.
10. R. P. Roesser, "A Discrete State Space Model for Linear Image Processing," IEEE Trans. Autom. Control, vol. 20, pp. 1-10, 1975.
11. M. G. Safonov and R. Y. Chiang, "A Schur method for balancedtruncation model reduction," IEEE Trans. Autom. Control, vol. 34, pp. 729-733, 1989.
12. M. S. Tombs and I. Postlethwaite, "Truncated balanced realization of a stable non-minimal state-space system," Int. J. Contr., vol. 46, pp. 1319-1330, 1987.
13. L. Pernebo and L. M. Silverman, "Model reduction via balanced state space representations," IEEE Trans. Autom. Control, vol. AC-27, pp. 382-387, 1982.
14. R. Treasure, A. Ghafoor, V. Sreeram, and K. Ngan, "Frequency weighted identification and model reduction of 2-D separable denominator systems," in Proc. 6th Int. Conf. Opt. Techn. Appl., Ballarat, Australia, Dec. 9-11, 2004.
15. A. Varga, A. El Moudni, P. Borne, and S. G. Tzafestas, Eds., "Efficient minimal realization procedure based on balancing," in Proc. IMACS Symp. Modelling Contr. Technol. Syst., Lille, France, 1991, vol. 2, pp. 42-47, Preprints.
16. A. Varga and B. D. O. Anderson, "Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction," Automatica, vol. 39, pp. 919-927, 2003.
17. D. Wang and A. Zilouchian, "Corrections and comments to 'model reduction of discrete linear systems via frequency-domain balanced structure," IEEE Trans. Circuits Syst. I, vol. 54, pp. 683-684.
18. G. Wang, V. Sreeram, and W. Q. Liu, "A new frequency-weighted balanced truncation method and an error bound," IEEE Trans. Autom. Control vol. 44, no. 9, pp. 1734-1737, 1999.
19. D.Wang, "Identification and approximation of 1-D and 2-D digital filters," Ph.D. dissertation, Florida Atlantic Univ., Boca Raton, FL, 1998.
20. D. Wang and A. Zilouchian, "Model reduction of discrete linear systems via frequency domain balanced realization," IEEE Trans. Circuits Syst. I, Fund. Theory Appl., vol. 47, no. 6, pp. 830-837, 2000.
21. K. Zhou, Y. Li, and E. B. Lee, "Model reduction of 2-D systems with frequency error bounds," IEEE Trans. Circuits Syst. II: Analog Digit. Signal Process., vol. 40, no. 2, pp. 107-110, 1993.