Strong stabilization of MIMO systems via unimodular interpolation in H∞

International Journal of Control

Volumn 69, Issue 6, 1998, Pages 797-818

  Saif, Abdul Wahid A ^a   Gu, Da Wei ^b   Postlethwaite, Ian ^b  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

STABILIZATION;

FACTORIZATION; MIMO SYSTEMS; STRONG STABILIZATION;

MULTIVARIABLE CONTROL SYSTEMS;

EID: 0032050434     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/002071798222550     Document Type: Article

References (34)

1. Chang, B. C., and Pearson, J. B., 1984, Optimal disturbance reduction in linear multivariable systems. IEEE Trans. Automat. Contr., 29, 880-887.
2. Chang, B. C., and Banda, S., 1989, Optimal H° norm computation for multivariable systems with multiple zeros. IEEE Trans. Automat. Contr., 34, 553-557.
3. Chen, H. B., Chow, J. H., Kale, M. A., and Minto, D., 1995, Simultaneous stabilization using stable system inversion. Automatica, 31, 531-542.
4. Chu, C.-C., and Doyle, J., 1984, On inner-outer and spectral factorizations. Proceedings of 23rd Conference on Decision and Control. Las Vegas, NV, USA, pp. 1764-1765.
5. Delsarte, Ph., Genin, Y., and Kamp, Y., 1979, The Nevanlinna-Pick problem for matrixvalued functions. SIAM J. Appl. Math. 36, 47-61.
6. Dorato, P., and Li, Y., 1986, A modification of the classical Nevanlinna-Pick interpolation algorithm with application to robust stabilization. IEEE Trans. Automat. Contr., 31, 645-648.
7. Dorato, P., Park, H.-B., and Li, Y., 1989, An algorithm for interpolation with units in H∞ with application to feedback stabilization. Automatica, 25, 427-430.
8. Doyle, J. C., 1984, Advances in Multivariable Control. Lecture Notes at ONR/Honeywell Workshop, Minneapolis, MN.
9. Francis, B. A., 1987, A Course in H∞ Control Theory (Springer-Verlag).
10. ∞-optimization with stable controllers. Automatica, 25, 629-634.
11. Halevi, Y., 1994, Stable LQG controllers. IEEE Trans. on Automatic Control, 39, 2104-2106. Also appeared in American Control Conference, 1987.
12. Halevi, Y., Bernstein, D., and Haddad, W., 1991, On stable full-order and reduced-order LQG controllers. Optimal Control Appl. & Methods, 12, 163-172.
13. Hara, S., and Sugie, T., 1991, Inner-outer factorization for strictly proper functions with jω zeros. Systems & Control Letters, 16, 179-185.
14. Ito, H., Ohmori, H., and Sano, A., 1993, Design of stable controllers attaining low H∞ weighted sensitivity. IEEE Trans. on Automatic Control, 38, 485-488.
15. Jacobus, M., Jamshidi, M., Abdallah, C., Dorato, P., and Bernstein, D., 1990, Suboptimal strong stabilization using fixed order dynamic compensator. American Control Conference, pp. 2659-2660.
16. Kimura, H., 1984, Robust stabilization for a class of transfer functions. IEEE Trans. Automat. Contr., 29, 788-793.
17. Maciejowski, J. M., 1989, Multivariable Feedback Design (Addison-Wesley).
18. Minto, K. D., and Vidyasagar, M., 1986, A state-space appraoch to simultaneous stabilization. Control Theory and Advanced Technology, 2, 39-64.
19. Nett, C. N., Jacobson, C. A., and Balas, M. J., 1984, A connection between state-space and doubly coprime fractional representations. IEEE Trans. Control, 29, 831-832.
20. O’ Young, S. D., and Francis, B., 1985, Sensitivity trade-offs for multivariable plants. IEEE Trans. Automat. Contr., 30, 625-632.
21. Patel, R. V., and Minro, N., 1982, Multivariable System Theory and Design (Oxford: Pergamon Press).
22. Saif, A.-W. A., 1995, Simultaneous stabilization of multivariable linear systems. Ph.D. Thesis, University of Leicester, UK.
23. Sideris, A., and Safonov, M. G., 1985, Infinity-norm optimization with a stable controller. Proceedings of American Control Conference, pp. 804-805.
24. Silverman, L. M., 1969, An algorithmfor inverting linear systems. IEEE Trans. on Automatic Control, 14, 270-276.
25. Tannenbaun, A., 1982, Modified Nevanlinna-Pick interpolation and feedback stabilization of linear plants with uncertainty in the gain factor. Int. J. Control, 36, 331-336.
26. Vidyasagar, M., 1985, Control System Synthesis: A Factorization Approach (Cambridge, Massachusetts: MIT Press).
27. ∞-suboptimal stable stabilization. Proceedings of the 32nd Conference on Decision and Control, San Antonio, TX, USA, pp. 1828-1829.
28. Wei, K., 1990, Stabilization of linear plant via a stable compensator having no real unstable zeros. Systems & Control Letters, 15, 259-264.
29. Yeh, F.-B., and Hwang, T.-S., 1989, A modification of the Nevanlinna algorithm on the solution of the H^x«-optimization problem. IEEE Trans. on Automatic Control, 34, 627-629.
30. Yeh, F.-B., and Wei, L. F., 1990, Inner-outer factorizations of right-invertible real-rational matrices. Systems & Control Letters, 14, 31-36.
31. Youla, D. C., Bongiorno, J. J., and Lu, C. N., 1974, Single-loop feedback stabilization of linear multivariable dynamic plants. Automatic, 10, 159-173.
32. Zames, G., 1981, Feedback and optimal sensitivity: model reference transformations, multiplicative semi-norms, and approximate inverses. IEEE Trans. on Automatic Control, 26, 301-320.
33. Zames, G., and Francis, B. A., 1983, Feedback, minimax sensitivity, and optimal robustness. IEEE Trans. on Automatic Control, 28, 585-601.
34. Zhang, Z., and Freudenberg, J. S., 1989, State-space formulas for inner-outer factorization. Proc. American Control Conference, 765-766.