Robust performance analysis for systems with structured uncertainty

International Journal of Robust and Nonlinear Control

Volumn 6, Issue 2, 1996, Pages 85-99

  Iwasaki, Tetsuya ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Linear matrix inequality; Q stability; Robust performance; Structured uncertainty

Indexed keywords

CONTROL; ERROR DETECTION; LINEAR ALGEBRA; MATRIX ALGEBRA; SYSTEMS ANALYSIS; TIME VARYING SYSTEMS;

LINEAR MATRIX INEQUALITY; ROBUST PERFORMANCE; STRUCTURED UNCERTAINTY;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 0030106953     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199603)6:2<85::AID-RNC137>3.0.CO;2-Z     Document Type: Article

References (34)

1. Apkarian, P., J. P. Chretien, P. Gabinet and J. M. Biannic, 'μ synthesis by D-K iterations with constant scaling', Proc. American Contr. Conf., San Francisco, June, 1993, pp. 3192-3196.
2. Barmish, B. R., 'Necessary and sufficient conditions for quadratic stabilizability of an uncertain linear system', J. Optimiz. Theory Appl., 46(4), 399-408 (1985).
3. Beck, C., 'Computational issues in solving LMIs', Proc. IEEE Conf. Decision Contr., Brighton, December, 1991, pp. 1259-1260.
4. Bernstein, D. S. and W. M. Haddad, 'Robust stability and performance analysis for state-space systems via quadratic Lyapunov bounds', SIAM J. Mat. Anal. Appl., 11(2), 239-271 (1990).
5. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, monograph in preparation.
6. Braatz, R. D., P. M. Young, J. C. Doyle and M. Morari, 'Computational complexity of μ calculation', Proc. American Contr. Conf., San Francisco, June, 1993, pp. 1682-1683.
7. Corless, M., G. Zhu and R. E. Skelton, 'Robustness of covariance controllers', Proc. IEEE Conf. Decision Contr., Tampa. December, 1989, pp. 2667-2672.
8. Doyle, J. C., 'Analysis of feedback systems with structured uncertainties', IEE Proc., 129, Part D(6), 242-250 (1982).
9. Doyle, J. C., 'Synthesis of robust controllers and filters', Proc. IEEE Conf. Decision Contr., Albuquerque, December, 1983, pp. 109-114.
10. Doyle, J. C., 'Structured uncertainty in control system design', Proc. IEEE Conf. Decision Contr., Fort Lauderdale, December, 1985, pp. 260-265.
11. Doyle, J. C. and A. Packard, 'Uncertain multivariable systems from a state space perspective', Proc. American Contr. Conf., Minneapolis, June, 1987, pp. 2147-2152.
12. Doyle, J. C., A. Packard and K. Zhou, 'Review of LFTs, LMIs, and μ', Proc. IEEE Conf. Decision Contr., Brighton, December, 1991, pp. 1227-1232.
13. Fan, M. and A. Tits, 'm-Form numerical range and the computation of the structured singular value', IEEE Trans. Automatic Control, AC-33(3), 284-289 (1988).
14. Fan, M., A. Tits and J. Doyle, 'Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics', IEEE Trans. Automatic Control, AC-36(1), 25-38.
15. Fan, M. K. H. and A. L. Tits, 'Characterization and efficient computation of the structured singular value', IEEE Trans. Automatic Control, AC-31(8), 734-743 (1986).
16. Kalman, R. E., 'Contributions to the theory of optimal control', Bol. Soc. Mat. Mexicana, 102-119 (1960).
17. ∞ control theory', IEEE Trans. Automatic Control, AC-35(3), 356-361 (1990).
18. ∞ control: a convex optimization approach', IEEE Trans. Automatic Control, AC-36(7), 824-837 (1991).
19. Leitmann, G., 'Guaranteed asymptotic stability for some linear systems with bounded uncertainties', J. Dyn. Sys., Meas. Contr., 101, 202-216 (1979).
20. ∞ control design', Proc. IEEE Conf. Decision Contr., Tampa, December, 1989, pp. 923-925.
21. Madiwale, A. N., 'Reduction of conservatism in worst case designs: systems with block diagonal uncertainty structure', Proc. American Contr. Conf., Pittsburgh, June, 1989, pp. 770-771.
22. Packard, A. and J. Doyle, 'The complex structured singular value', Automatica, 29(1), 71-109 (1993).
23. Packard, A. and J. C. Doyle, 'Quadratic stability with real and complex perturbations', IEEE Trans. Automatic Control, AC-35(2), 198-201 (1990).
24. Packard, A., K. Zhou, P. Pandey, J. Leonhardson and G. Balas, 'Optimal, constant I/O similarity scaling for fullinformation and state-feedback control problems', Sys. Contr. Lett., 19, 271-280 (1992).
25. Petersen, I. R., 'A Riccati equation approach to the design of stabilizing controllers and observers for a class of uncertain linear systems', IEEE Trans. Automatic Control, AC-30(9), 904-907 (1985).
26. Petersen, I. R. and D. C. McFarlane, 'Optimizing the guaranteed cost in the control of uncertain linear systems', Robustness of Dynamic Systems with Parameter Uncertainties, Birkhäuser Verlag Basel, 1992, pp. 241-250.
27. 2 control problem', Automatica, 29(2), 373-386 (1993).
28. Rotea, M. A., M. Corless, D. Da and I. R. Petersen, 'Systems with structured uncertainty: relations between quadratic and robust stability', IEEE Trans. Automatic Control, AC-38(5), 799-803 (1993).
29. Safonov, M. G., 'Stability margins of diagonally perturbed multivariable feedback systems', IEE Proc., 129, Part D(6), 251-256 (1982).
30. ∞-optimal sensitivity vs. stability margin', Proc. IEEE Conf. Decision Contr., Albuquerque, December, 1983, pp. 115-118.
31. 2 control problem: a worst case design', IEEE Trans. Automatic Control, AC-38(9), 1358-1370 (1993).
32. Wilson, D. A., 'Convolution and Hankel operator norms for linear systems', IEEE Trans. Automatic Control, AC-34(1), 94-98 (1989).
33. ∞ control and quadratic stabilization of systems with parameter uncertainty via output feedback', IEEE Trans. Automatic Control, AC-37(8), 1253-1256 (1992).
34. ∞ optimization', Sys. Contr. Lett., 11, 85-92 (1988).