Fixed-order scaled ℋ∞ synthesis

Optimal Control Applications and Methods

Volumn 18, Issue 6, 1997, Pages 381-398

  Iwasaki, Tetsuya ^a   Rotea, Mario A ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b Purdue University   (United States)

Author keywords

Fixed order control; Linear matrix inequality; Robust control; control

Indexed keywords

ALGORITHMS; CONTROL SYSTEM SYNTHESIS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

FIXED ORDER CONTROLLERS; LINEAR MATRIX INEQUALITY;

OPTIMAL CONTROL SYSTEMS;

EID: 0031274485     PISSN: 01432087     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1514(199711/12)18:6<381::AID-OCA607>3.0.CO;2-V     Document Type: Article

References (37)

1. Doyle, J., 'Analysis of feedback systems with structured uncertainties', IEE Proc. Part D, 129(6), 242-250 (1982).
2. Safonov, M. G., 'Stability margins of diagonally perturbed multivariable feedback systems', IEE Proc. Part D, 129(6), 251-256 (1982).
3. Doyle, J., 'Synthesis of robust controllers and filters', Proc. IEEE Conf. Dec. Control, San Antonio, Texas, 1983.
4. ∞ optimal sensitivity vs. stability margin', Proc. IEEE Conf. Dec. Control. San Antonio, Texas, 1983, pp. 115-118.
5. Safonov, M. G., 'Optimal diagonal scaling for infinity-norm optimization', Systems Control Lett., 7(1), 257-260 (1986).
6. Balakrishnan, V., 'Solving interpolation problems via generalized eigenvalue minimization', preprint, (1993).
7. El Ghaoui, L., V. Balakrishnan, E. Feron and S. P. Boyd, 'On maximizing a robustness measure for structured nonlinear perturbations', Proc. American Contr. Conf., 2923-2924 (1992).
8. Iwasaki T., 'A unified matrix inequality approach to linear control design', Ph.D. Dissertation, Purdue University, West Lafayette, IN, U.S.A., (1993).
9. Packard, A., K. Zhou, P. Pandey, J. Leonhardson and G. Balas, 'Optimal, constant I/O similarity scaling for full-information and state-feedback control problems', Systems Control Lett., 19(4), 271-280 (1992).
10. Rotea, M. A., and R. K. Prasanth, The ρ performance measure: A new tool for controller design with multiple frequency domain specifications', Proc. American Control Conf, 1994.
11. Goh, K.-C., M. G. Safonov and G. P. Papavassilopoulos, 'A global optimization approach for the BMI problem', Proc. IEEE Conf. Decision Control, 2009-2014 (1994).
12. ∞ control problem', Proc. American Control Conf., (1995).
13. Hyland, D. C. and D. S. Bernstein, The optimal projection equations for fixed-order dynamic compensation', IEEE Trans. Auto. Control, 29, 1034-1037 (1984).
14. Makila, P. M. and H. T. Toivonen, 'Computational methods for parametric LQ problems - A survey', IEEE Trans. Auto. Control, 32(8), 658-671 (1987).
15. m-synthesis via bilinear matrix inequalities', Proc. IEEE Conf. Decision Control, 2032-2037 (1994).
16. Rotea, M. A. and T. Iwasaki, 'An alternative to the D-K iteration?', Proc. American Control Conf., 1994, pp. 53-57.
17. Boyd, S. and L. El Ghaoui, 'Method of centers for minimizing generalized eigenvalues', Linear Algebra Appl., 188&189, 63-111 (1993)
18. Nesterov, Yu. and A. Nemirovsky, Interior point polynomial methods in convex programming: Theory and applications, SIAM (1993).
19. Wie, B. and D. S. Bernstein, 'A benchmark problem for robust control design', Proc. American Control Conf., 961-962 (1990)
20. Wie, B. and D. S. Bernstein, 'Benchmark problems for robust control design', Proc. American Control Conf., 1929-1930 (1991).
21. Wie, B. and D. S. Bernstein, 'Benchmark problems for robust control design', Proc American Control Conf., 2047-2048 (1992).
22. Wie, B. and D. S. Bernstein, 'Benchmark problems for robust control design', AIAA J. Guid. Control Dyn., 15(5), 1057-1059 (1992).
23. ∞ synthesis using a bilinear pole shifting transform', AIAA J. Guid. Control Dyn., 15(5), 1111-1117 (1992)
24. Braatz, R. and M. Morari, 'Robust control for a noncollocated spring-mass system', AIAA J. Guid. Control Dyn., 15(5), 1103-1110 (1992).
25. Packard, A., K. Zhou, P. Pandey and G. Becker, 'A collection of robust control problems leading to LMIs', Proc IEEE Conf. Decision Contr, 1245-1250 (1991).
26. Iwasaki, T. and R. E. Skelton, The XY-centering algorithm for the dual LMI problem: a new approach to fixed order control design', Int. J. Control, 62(6), 1257-1272 (1995).
27. Boyd, S., L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in system and control theory, SIAM Studies in Applied Mathematics, Philadelphia (1994).
28. Packard, A. and J. Doyle, The complex structured singular value', Automatica, 29(1), 71-109 (1993).
29. Boyd, S. and Q. Yang, 'Structured and simultaneous Lyapunov functions for system stability problems', Int. J. Control 49, 2215-2240 (1989)
30. El Ghaoui, L. and P. Cabinet, 'Rank minimization under LMI constraints: a framework for output feedback problems', Proc. European Control Conf., 1176-1179 (1993).
31. Fu, M., L. Xie and C. E. de Souza, Control of uncertain dynamic systems, S. P. Bhattacharyya and L. H. Keel, CPC Press, 1991, pp. 63-76.
32. ∞ control problem: LMI existence conditions and state space formulas', Automatica, 30(8), 1307-1317 (1994).
33. ∞ control theory', IEEE Trans. Auto. Control. 35(3), 356-361 (1990).
34. Megretski, A., 'Necessary and sufficient conditions of stability: a multiloop generalization of the circle criterion', IEEE Trans. Auto. Control, 38(5), 753-756 (1993).
35. Shamma, J. S., 'Robust stability with time-varying structured uncertainty', IEEE Trans. Automat. Control, 39(4), 714-724 (1994).
36. Tikku, A. and K. Poolla, 'Robust performance against slowly-varying structured perturbations', Proc. IEEE Conf. Dec. Control, 990-995 (1993).
37. Zhou, K., P. P. Khargonekar, J. Stoustrup and H. H. Niemann, 'Robust stability and performance of uncertain systems in state space', Proc. IEEE Conf. Dec. Control, 662-667 (1992)