Balanced Gains and Their Significance for L2 Model Reduction

IEEE Transactions on Automatic Control

Volumn 30, Issue 7, 1985, Pages 690-693

  Kabamba, P T ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS;

BALANCED GAINS; IMPULSE RESPONSE; MODEL REDUCTION; SUBOPTIMAL BALANCED TRUNCATION CRITERION;

CONTROL SYSTEMS;

EID: 0022099579     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1985.1104017     Document Type: Article

References (24)

1. B. C. Moore, “Principal component analysis in linear systems: Controllability, observability, and model reduction,” IEEE Trans. Automat. Contr., vol. AC-26, pp. 17–31, Jan. 1981.
2. L. M. Silverman, S. Shokoohi, and P. Van Dooren, “Balanced realization and approximation of time-variable systems,” in Proc. Int. Symp. Math. Theory Networks Syst., vol. 3, Delft Univ. Technol., Delft, The Netherlands, July 3–6, 1979.
3. L. Pernebo, and L. M. Silverman, “Balanced system and model reduction,” in Proc. I8th Conf. Decision Contr., Ft. Lauderdale, FL, Dec. 12–14, 1979.
4. “Model reduction via balanced state space representations,” IEEE Trans. Automat. Contr., vol. AC-27, pp. 382–287, Feb. 1982.
5. L. M. Silverman, and M. Bettayeb, “Optimal approximation of linear systems,” in Proc. Joint Automat. Contr. Conf., San Francisco, CA, 1980.
6. A. J. Laub, “On computing balancing transformations, in Proc. Joint Automat. Contr. Conf., San Francisco, CA, 1980.
7. A. Yousuff and R. E. Skelton, “A note on balanced controller reduction,” IEEE Trans. Automat. Contr., vol. AC-29, pp. 254–257, Mar. 1984.
8. E. I. Verriest, “Suboptimal LQC-design and balanced realizations,” in Proc. 20th IEEE CDC, San Diego, CA, Dec. 1981, pp. 686–687.
9. E. A. Jonckheere and L. M. Silverman. “A new set of invariants for linear systems—Applications to reduced-order compensator design,” IEEE Trans. Automat. Contr., vol. AC-28, pp. 953–964, Oct. 1983.
10. J. A. Davis and R. E. Skelton, “Another balanced controller reduction algorithm,” Syst. Contr. Lett., 1984, to be published.
11. C. T. Chen, Introduction to Linear Systems Theory. New York: Holt. Rinehart, Winston, 1970.
12. P. T. Kabamba, “Balanced forms. Canonicity and parametrization,” IEEE Trans. Automat. Contr., submitted for publication.
13. “Balanced gains and their significance for balanced model reductions,” presented at the 18th Conf. Inform. Sci. Syst., Princeton, NJ, Mar. 1984.
14. D. A. Wilson, “Optimal solution of model reduction problem,” in Proc. IEE, vol. 17, pp. 1161–1165, June 1970.
15. “Model reduction of multivariable systems,” Int. J. Contr., vol. 20, pp. 57–64, Jan. 1974.
16. F. D. Galiana, “On the approximation of multiple input-multiple output constant linear systems,” Int. J. Contr., vol. 17, no. 6, pp. 1313–1324, 1973.
17. J. B. Briggs and T. F. Edgar, “Least squares reduction of linear systems using impulse response,” Int. J. Contr., vol. 20, no. 2, pp. 213–223, 1974.
18. J. D. Aplevich, “Approximation of discrete linear systems,” Int. J. Contr., vol. 17, no. 3, pp. 565–575, 1973.
19. G. Hirzinger and G. Kriesselmeier, “On optimal approximation of high-order linear systems by low-order models,” Int. J. Contr., vol. 22. no. 3, pp. 339–408, 1975.
20. D. A. Wilson and R. N. Mishra, “Optimal reduction of multivariable systems,” Int. J. Contr., vol. 29, no. 3, pp. 267–278, 1979.
21. R. N. Mishra and D. A. Wilson, “A new algorithm for optimal reduction of multivariable systems,” Int. J. Contr., vol. 31, no. 3, pp. 443–466, 1980.
22. D. A. Wilson and R. N. Mishra, “Design of low-order estimation using reduced-order models,” Int. J. Contr., vol. 29, no. 3, pp. 447–456, 1979.
23. K. Glover and D. J. N. Limebeer, “Robust multivariable control system design using optimal reduced-order plant models,” in Proc. 1983 Automat. Contr. Conf., San Francisco, CA, June 1983, pp. 644–649.
24. D. Enns, “Model reduction based on frequency response for control system design,” presented at the NASA/JPL Workshop on Ident. and Contr. Flexible Space Struct., San Diego, CA, June 1984.