A time-limited balanced reduction method

Proceedings of the IEEE Conference on Decision and Control

Volumn 5, Issue , 2003, Pages 5250-5253

  Gugercin, Serkan ^a   Antoulas, Athanasios C ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b Rice University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; ERRORS; FUNCTIONS; LINEAR SYSTEMS; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA;

LINEAR TIME INVARIANT DYNAMICAL SYSTEMS; SQUARE ROOTS;

CONTROL SYSTEMS;

EID: 1542289892     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2003.1272471     Document Type: Conference Paper

References (25)

1. A.C. Antoulas, Lectures on the approximation of linear dynamical systems, Draft, to appear, SIAM Press 2002.
2. A. C. Antoulas, D. C. Sorensen, and S. Gugercin, A survey of model reduction methods for large scale systems. Contemporary Mathematics, AMS Publications, 280: 193-219, 2001.
3. P. Benner, E. S. Quintana-Orti, and G. Quintana-Orti, Efficient Numerical Algorithms for Balanced Stochastic Truncation, International Journal of Applied Mathematics and Computer Science, Special Issue: Numerical Analysis and Systems Theory, Editor Stephen L. CAMPBELL, Vol. 11, No. 5, 2001.
4. U.B. Desai and D. Pal, A transformation approach to stochastic model reduction, IEEE Trans. Automat. Contr., vol AC-29, 1984.
5. rd IEEE Conf. Decision and Control, 1984.
6. K. Gallivan, P. Van Dooren, and E. Grimme, A rational Lanczos algorithm for model reduction, Numerical Algorithms, 2(1-2):33-63, April 1996.
7. K. Gallivan, P. Van Dooren, and E. Grimme, On some recent developments in projection-based model reduction, in ENU-MATH 97 (Heidelberg), World Sci. Publishing, River Edge, NJ, 1998, pp. 98-113, 1998.
8. W. Gawronski and J.-N. Juang, Model reduction in limited time and frequency intervals, Int. J. Systems Sci., vol. 21, No. 2, pp. 349-376, 1990.
9. M. Green, A relative error bound for balanced stochastic truncation, IEEE Trans. Automat. Contr., vol. AC-33, No. 10, pp. 961-965.
10. M. Green, Balanced stochastic realizations, Journal of Linear Algebra and its Applications, Vol. 98, pp. 211-247, 1988.
11. S. Gugercin and A. C. Antoulas, A comparative study of 7 model reduction algorithms, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December 2000.
12. S. Gugercin, D.C. Sorensen and A.C. Antoulas, A modified low-rank Smith method for large-scale Lyapunov equations, Numerical Algorithms, Vol. 32, Issue 1, pp. 27-55, January 2003.
13. S. Gugercin and A.C. Antoulas, A survey of balancing methods for model reduction, Proceedings of European Control Conference ECC2003, September 2003.
14. E.A. Jonckheere and L.M. Silverman, A new of invariants for linear system - application to reduced order compensator design, IEEE Trans. Automat. Contr.. vol. AC-28, No. 10, pp. 953-964, 1983.
15. T. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, NJ, 1980.
16. C.-A Lin and T.-Y Chiu, Model reduction via frequency weighted balanced realization, Control Theory and Advanced Technol., vol. 8, pp. 341-351, 1992.
17. B.C. Moore, Principal Component Analysis in Linear System: Controllability, Observability and Model Reduction, IEEE Transactions on Automatic Control, AC-26:17-32, 1981.
18. C. T. Mullis and R. A. Roberts, Synthesis of minimum roundoff noise fixed point digital filters, IEEE Trans. on Circuits and Systems, CAS-23:, pp: 551-562, 1976.
19. R. Ober, Balanced parameterization of classes of linear systems, SIAM J. Cont. App., 1991.
20. P.C. Opdenacker and E.A. Jonckheere, A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds, IEEE Trans. Circuits and Systems, 1988.
21. th IEEE Conf. Decision and Control, 1995.
22. G. Wang, V. Sreeram and W.Q. Liu, A new frequency weighted balanced truncation method and an error bound, IEEE Trans. Automat. Contr., Vol. 44, No. 9, pp. 1734-1737, 1999.
23. W. Wang and M.O. Safanov, Multiplicative-error bound for balanced stochastic truncation model reduction, IEEE Trans. Automat. Contr., vol. AC-37, No. 8, pp. 1265-1267, 1992.
24. th IEEE Conference on Decision and Control, 2000.
25. ∞ norm and optimal Hankel norm model reduction, IEEE Trans. Automat. Contr., vol. 40, No. 10, pp. 1687-1699, 1995.