Fast algorithm for the computation of an upper bound on the μ-norm

Automatica

Volumn 36, Issue 3, 2000, Pages 449-456

  Lawrence, Craig T ^a   Tits, André L ^b,c,d,e   Van Dooren, Paul M ^c,f  

^a Alphatech Inc   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e UNIVERSITY OF MARYLAND   (United States)

^f UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL METHODS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS; TRANSFER FUNCTIONS; UNCERTAIN SYSTEMS;

STRUCTURED SINGULAR VALUE; TIME VARYING UNCERTAINTY; UNCERTAIN LINEAR SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 0034159737     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(99)00165-X     Document Type: Article

References (24)

1. Balas, G. J., Doyle, J. C., Glover, K., Packard, A., & Smith, R. (1993). μ-analysis and synthesis toolbox: user's guide. MUSYN Inc. and The Math Works, Inc.
2. Barzilai, J., & Ben-Tal, A. (1982). Nonpolynomial and inverse interpolation for line search: synthesis and convergence rates. SIAM Journal of Numerical Analysis, 19(6), 1263-1277.
3. Bercovici, H., Foias, C., & Tannenbaum, A. (1990). Structured interpolation theory. In I. Gohberg (Ed.), Extension and interpolation of linear operators and matrix functions Operator Theory, Advances and Applications, Vol. 47. Boston: Birkhauser (pp. 195-220).
4. ∞-norm. Systems and Control Letters, 15, 1-7.
5. Boyd, S. P., El Ghaoui, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia: SIAM.
6. ∞-norm of a transfer function matrix. Systems and Control Letters, 14(5), 287-293.
7. Doyle, J. C., & Packard, A. (1987). Uncertain multivariable systems from a state space perspective. Proceedings of the American control conference (pp. 2147-2152). Minneappolis.
8. ∞ performance and of largest acceptable uncertainty. Systems and Control Letters, 18, 409-421.
9. Feron, E. (1997). A more reliable robust stability indicator for linear systems subject to parametric uncertainties. IEEE Transactions on Automatic Control, 42(9), 1326-1330.
10. Ferreres, G., & Fromion, V. (1997). Computation of the robustness margin with the skewed μ tool. Systems and Control Letters, 32, 193-202.
11. Gahinet, P., Nemirovski, A., Laub, A. L., & Chilali, M. (1995). LMI control toolbox - for use with MATLAB. The Math Works, Inc.
12. Hinrichsen, D., & Son, N. K. (1989). The complex stability radius of discrete-time systems and simplectic pencils. Proceedings of the Conference on Decision and Control, Tampa (pp. 2265-2270).
13. Lawrence, C. T., Tits, A. L., & Van Dooren, P. (1996). A fast algorithm for the computation of an upper bound on the μ-norm. Proceedings of the IFAC World Congress, San Francisco, Vol. H. (pp. 59-64).
14. Lee, L., & Tits, A. L. (1993). On continuity/discontinuity in robustness indicators. IEEE Transactions on Automatic Control, AC-38(10), 1551-1553.
15. Packard, A., & Doyle, J. C. (1993). The complex structured singular value. Automatica, 29, 71-109.
16. Poolla, K., & Tikku, A. (1995). Robust performance against time-varying structured perturbations. IEEE Transactions on Automatic Control, AC-40(9), 1589-1602.
17. Sideris, A. (1992). Elimination of frequency search from robustness tests. IEEE Transactions on Automatic Control, AC-37(10), 1635-1640.
18. Sreedhar, J., Van Dooren, P., & Tits, A. L. (1996). A fast algorithm to compute the real structured stability radius. In R. Jeltsch, M. Mansour (Eds.). Stability theory: proceedings of centenary conference, Ticino, Switzerland, May 21-26, (pp. 219-230). Boston: Birkhäuser.
19. Stewart, G. W., & Sun, J. (1990). Matrix perturbation theory. New York: Academic Press.
20. Tits, A. L., & Balakrishnan, V. (1998). Small-μ theorems with frequency-dependent uncertainty bounds. Mathematics of Control Signals and Systems, 11(3), 220-243.
21. Tits, A. L., & Fan, M. K. H. (1995). On the small-μ theorem. Automatica, 31(8), 1199-1201.
22. Toker, O., & Özbay, H. (1995). On the NP-hardness of the purely complex μ computation, analysis/synthesis, and some related problems in multi-dimensional systems. Proceedings of the American Control Conference (pp. 447-451).
23. Zhou, K., & Doyle, J. C. (1998). Essentials of robust control. Englewood Cliffs, NJ: Prentice-Hall.
24. Zhou, K., Doyle, J. C., & Glover, K. (1995). Robust and optimal control. Englewood Cliffs, NJ: Prentice Hall.