Model reduction of uncertain systems retaining the uncertainty structure

Systems and Control Letters

Volumn 54, Issue 8, 2005, Pages 771-779

  Dolgin, Yuri ^a   Zeheb, Ezra ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Linear semi infinite programming; Linear in parameters interval systems; Model reduction; Uncertain systems

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; DISCRETE TIME CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR PROGRAMMING; PARAMETER ESTIMATION; POLYNOMIALS;

LINEAR SEMI-FINITE PROGRAMMING; LINEAR SEMI-INFINITE PROGRAMMING; LINEAR-IN-PARAMETERS INTERVAL SYSTEMS; MODEL REDUCTION;

UNCERTAIN SYSTEMS;

EID: 20344388091     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2004.10.010     Document Type: Article

References (25)

1. E.J. Anderson, and P. Nash Linear Programming in Infinite-Dimensional Spaces 1987 Wiley New York
2. E. Assuncao, P.L.D. Peres, H 2 and/or H ∞ -norm model reduction of uncertain discrete-time systems, Proceedings of the ACC, San Diego, June 1999, pp. 4466-4470.
3. B. Bandyopadhyay, O. Ismail, and R. Gorez Routh-pade approximation for interval systems IEEE Trans. Automat. Control 39 1994 2454 2456
4. C.L. Beck, J. Doyle, and K. Glover Model reduction of multi-dimensional and uncertain systems IEEE Trans. Automat. Control 41 1996 1466 1477
5. N. Cohen, A. Levkovich, E. Zeheb, and P. de Oliveira Frequency response envelopes of a family of uncertain discrete-time systems Circuits, Systems, and Signal Process. 22 2003 19 41
6. M. Diab, W.-Q. Liu, and V. Sreeram A new approach for frequency weighted L 2 model reduction of discrete-time systems Optimal Control Appl. Methods 19 1998 147 167
7. Y. Dolgin, and E. Zeheb Model reduction of uncertain systems approximation by fixed-coefficients system IEEE Trans. Automat. Control 51 2004 406 411
8. M.C. Ferris, and A.B. Philpott An interior point algorithm for semi-infinite linear programming Math. Programming 43 1989 257 276
9. L. Fortuna, A. Gallo, and G. Nunnari Model Order Reduction Techniques with Application in Electrical Engineering October 1992 Springer Berlin
10. L. Giarre, and M. Milanese SM identification of approximating models for H ∞ robust control Proceedings of the 35 CDC 4 1996 4184 4189
11. K. Glashoff, and S. Gustafson Linear Optimization and Approximation 1983 Springer Berlin
12. K. Glashoff, and K. Roleff A new method for Chebyshev approximation of complex-valued function Math. Comput. 36 153 1981 233 239
13. M.A. Goberna, and M.A. Lopez Linear Semi-Infinite Optimization 1998 Wiley New York
14. I. Jikuya, H. Kimura, Representation and reduction of model sets, Proceedings of the 38th IEEE CDC Phoenix, AZ, December 1999, pp. 1482-1487.
15. L.J. Karam, and J.H. McClellan Complex Chebyshev approximation for FIR filter design IEEE Trans. Circ. Syst. II Analog and Digital Signal Process. 42 3 1995 207 216
16. G. Lastman, and N. Sinha A comparison of the balanced matrix method and the aggregation method of model reduction IEEE Trans. Automat. Control 30 3 1985 301 304
17. G. Obinata, and B.D.O. Anderson Model Reduction for Control System Design October 2001 Springer Berlin
18. Z. Qiu, S. Chen, and I. Elishakoff Bounds of eigenvalues for structures with an interval description of uncertain but not random parameters Chaos, Solitons, and Fractals 7 3 1996 425 434
19. R. Reemtsen, Jan-J Ruckmann, Semi-Infinite Programming, Nonconvex Optimization and Its Applications, vol. 25, Kluwer Academic Publishers, Dordrecht, 1998.
20. H. Rotstein, N. Galperin, and P.-O. Gutman Set membership approach for reducing value sets in the frequency domain IEEE Trans. Automat. Control 43 9 1998 1346 1350
21. Y. Shamash Model reduction using the Routh stability criterion and the Pade approximation technique Int. J. Control 21 3 1975 475 484
22. G. Wang, V. Sreeram, and W.Q. Liu Balanced performance preserving controller reduction Systems Control Lett. 46 2002 99 110
23. D. Wang, and A. Zilouchian Model reduction of discrete linear systems via frequency-domain balanced structure IEEE Trans. Circuits and Systems 47 6 2000 830 838
24. F. Wu, J. Jaramillo, Numerical algorithm for model reduction of polytopic uncertain linear systems, Proceedings of the ACC, Anchorage, May 2002, pp. 1748-1752.
25. K. Zhou Frequency-weighted L ∞ norm and optimal Hankel norm model reduction IEEE Trans. Automat. Control 40 1995 1687 1699