Model reduction of linear systems using extended balanced truncation

Proceedings of the American Control Conference

Volumn , Issue , 2008, Pages 4654-4659

  Sandberg, Henrik ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL THEORY; FOOD PRESERVATION; LINEAR CONTROL SYSTEMS; LINEAR SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; OBSERVABILITY; STANDARDS; SWITCHING SYSTEMS; UNCERTAIN SYSTEMS;

A-PRIORI; ADDITIONAL STRUCTURE; BALANCED TRUNCATION; DECISION VARIABLES; GRAMIANS; MODEL REDUCTIONS; MODEL STABILITY; STANDARD METHODS; WEIGHTED REDUCTION;

LINEAR MATRIX INEQUALITIES;

EID: 52449083358     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2008.4587229     Document Type: Conference Paper

References (19)

1. B. C. Moore, "Principal component analysis in linear systems: controllability, observability, and model reduction," IEEE Transactions on Automatic Control, vol. 26, no. 1, pp. 17-32, February 1981.
2. L. Pernebo and L. Silverman, "Model reduction via balanced state space representation," IEEE Transactions on Automatic Control, vol. 27, pp. 382-387, 1982.
3. D. Enns, "Model reduction with balanced realizations: an error bound and a frequency weighted generalization," in Proceedings of the IEEE Conference on Decision and Control, Las Vegas, Nevada, 1984.
4. ∞-error bounds," International Journal of Control, vol. 39, pp. 1115-1193, 1984.
5. U. Al-Saggaf and G. Franklin, "An error-bound for a discrete reduced-order model of a linear multivariable system," IEEE Transactions on Automatic Control, vol. 32, no. 9, pp. 815-819, 1987.
6. D. Hinrichsen and A. Pritchard, "An improved error estimate for reduced-order models of discrete-time systems," IEEE Transactions on Automatic Control, vol. 35, no. 3, pp. 317-320, 1990.
7. K. Zhou, C. D'Souza, and J. Cloutier, "Structurally balanced controller order reduction with guaranteed closed loop performance," Systems and Control Letters, vol. 24, pp. 235-242, 1995.
8. C. Beck, J. Doyle, and K. Glover, "Model reduction of multidimensional and uncertain systems," IEEE Transactions on Automatic Control, vol. 41, no. 10, pp. 1466-1477, October 1996.
9. L. Li and F. Paganini, "Structured coprime factor model reduction based on LMIs," Automatica, vol. 41, no. 1, pp. 145-151, Jan. 2005.
10. A. Vandendorpe and P. Van Dooren, Model Order Reduction: Theory, Research Aspects and Applications, ser. Mathematics in Industry Series. Springer Verlag, 2007, ch. Model reduction of interconnected systems.
11. H. Sandberg and R. M. Murray, "Model reduction of interconnected linear systems using structured Gramians," in Proccedings of the IFAC World Congess, 2008, to appear. Available from http://www.ee.kth.se/ ∼hsan/ifac2008.pdf.
12. M. De Oliviera, J. Bernussou, and J. Geromel, "A new discrete-time robust stability condition," Systems & Control Letters, vol. 37, pp. 261-265, 1999.
13. ∞ norm characterizations and controller parametrizations for discrete-time systems," International Journal of Control, vol. 75, no. 9, pp. 666-679, 2002.
14. M. Subbotin and R. Smith, "Design of a distributed decentralized estimator for a formation with fixed communication topology," in Proceedings of the 2007 American Control Conference, New York City, New York, July 2007, pp. 5025-5030.
15. _, "Distributed estimator design for a formation with Markovian communication topology," in Proceedings of the 2007 American Control Conference, New York City, New York, July 2007, pp. 5046-5051.
16. K. Zhou and J. Doyle, Essentials of Robust Control. Upper Saddle River, New Jersey: Prentice Hall, 1998.
17. J. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, vol. 11-12, pp. 625-653, 1999, available from http://fewcal.kub.nl/sturm/software/sedumi. html.
18. J. Löfberg, "YALMIP : A toolbox for modeling and optimization in MATLAB," in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004, available from http://control.ee.ethz.ch/∼joloef/yalmip.php.
19. P. Bendotti and C. Beck, "On the role of LFT model reduction methods in robust controller synthesis for a pressurized water reactor," IEEE Transactions on Control Systems Technology, vol. 7, no. 2, pp. 248-257, March 1999.