Filter design: A finite dimensional convex optimization approach

International Journal of Robust and Nonlinear Control

Volumn 13, Issue 14, 2003, Pages 1317-1335

  Rossignol, L ^a   Scorletti, G ^a   Fromion, V ^b  

^a UNIVERSITÉ DE CAEN   (France)

^b UNIV MONTPELLIER   (France)

Author keywords

Filter design; H control; Linear matrix inequalities; Optimization

Indexed keywords

FREQUENCY RESPONSE; IIR FILTERS; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; SIGNAL PROCESSING;

FILTER DESIGN; FINITE DIMENSIONAL CONVEX OPTIMIZATION APPROACH; LINEAR MATRIX INEQUALITIES;

CONTROL SYSTEM SYNTHESIS;

EID: 0346149990     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.854     Document Type: Article

References (31)

1. Rabiner L, Gold B. Theory and Application of Digital Signal Processing. Prentice-Hall: Englewood Cliffs, NJ, 1975.
2. Gorner S, Potchinkov A, Reemtsen R. The direct solution of nonconvex nonlinear fir filter design problems by a sip method. 1999, submitted.
3. Zames G. Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Transactions on Automatic Control 1981; AC-26(2):301-320.
4. ∞ control problems. IEEE Transactions on Automatic Control 1989; 34(8):831-847.
5. Zhou K, Doyle JC, Glover K. Robust and Optimal Control. Prentice-Hall: Englewood Cliffs, NJ, 1995.
6. Horowitz IM. Synthesis of Feedback Systems. Academic Press: New York, 1963.
7. Oustaloup A, Mathieu B, Lanusse P. The CRONE control of resonant plants: Application to a flexible transmission. European Journal of Control 1995; 1(2):113-121.
8. Desoer CA, Vidyasagar M. Feedback Systems: Input-Output Properties. Academic Press: New York, 1975.
9. ∞ et approche symbolique de la forme standard. Ph.D. Thesis, Université Paris XI Orsay, France, 1995.
10. Lanzon A, Cantoni M. A state-space algorithm for the simultaneous optimisation of performance weights and controllers in μ-synthesis. In Proceedings of the IEEE Conference on Decision and Control, Sydney, Australia, December 2000.
11. Lanzon A, Richards RJ. A frequency-domain optimisation algorithm for simultaneous design of performance weights and controllers in μ-synthesis. In Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, USA, December 1999; 4523-4528.
12. Parks TW, Mc Clellan JH. Chebyshey approximation for non recursive digital filters with linear phase. IEEE Transactions on Circuit Theory 1972; CT-19:189-194.
13. Parks TW, Mc Clellan JH. A program for the design of linear phase finite impulse response digital filters. IEEE Transactions on Acoustics, Speech and Signal Processing 1974; AU-21: 195-199.
14. Steiglitz K, Parks TW, Kaiser JF. METEOR: A constraint-based FIR filter design program. IEEE Transactions on Signal Processing, 1992; 40(8):1901.
15. Wu S-P, Boyd S, Vanderberghe L. FIR filter design via semidefinite programming and spectral factorization. In Proceedings of the IEEE Conference on Decision and Control, pp. 271-276.
16. Wu SP. Max-det programming with applications in magnitude. Ph.D. Thesis, Standford University, December 1997.
17. Rossignol L, Scorletti G, Fromion V. Filter design and related problems: a finite dimensional convex optimization approach. Technical Report LAP 02.02, LAP-ISMRA, Université de Caen, February 2002.
18. Popov VM. Hyperstability of Control Systems. Springer-Verlag: New York, 1973.
19. Fan MKH, Tits AL, Doyle JC. Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control 1991; 36(1):25-38.
20. Ly JH, Safonov MG, Chiang RY. Real/complex multivariable stability margin computation via generalized Popov multiplier-LMI approach. In Proceedings of the American Control, 1994.
21. Lu WM, Zhou K, Doyle JC. Stabilization of LFT systems. IEEE Transactions on Automatic Control 1996; p. 50-65.
22. Scorletti G, El Ghaoui L. Improved LMI conditions for gain scheduling and related problems. International Journal of Robust and Nonlinear Control 1998; 8(10):845-877.
23. Rabiner LR, Gold B (eds). Theory and Application of Digital Signal Processing. Prentice-Hall, inc., Englewood Cliffs. NJ, 1975.
24. ∞ Control Theory. Springer Verlag: NY, 1987.
25. Boyd S, El Ghaoui L. Method of centers for minimizing generalized eigenvalues. Linear Algebra and Applications, Numerical Linear Algebra Methods in Control, Signals and Systems, special issue 1993; 188:63-111.
26. Boyd S, El Ghaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Studies in Applied Mathematics. SIAM: Philadelphia, PA, June 1994.
27. Vandenberghe L, Boyd S. Semidefinite programming. SIAM Review 1996; 38(1):49-95.
28. El Ghaoui L, Nikoukhah R, Delebecque F. LMITOOL: A front-end for LMI optimization, user's guide, February 1995. Available via anonymous ftp to ftp.enstra.fr, under/pub/elghaoui/lmitool.
29. Gahinet P, Nemirovsky A, Laub AL, Chilali M. LMI Control Toolbox. The Mathworks Inc., 1995.
30. Meinsma G, Shrivastava Y, Fu M. A dual of mixed μ and on the losslessness of (D,G)-scaling. In Proceedings of the IEEE Conference on Decision and Control 1996; 1287-1292.
31. Iwasaki T, Meinsma G, Fu M. Generalized S-procedure and finite frequency KYP lemma. Mathematical Problems in Engineering 2000; 6:305-320.