Generalized ℓ2 synthesis

IEEE Transactions on Automatic Control

Volumn 44, Issue 6, 1999, Pages 1145-1156

  D'Andrea, Raffaello ^a  

^a Cornell University   (United States)

Author keywords

Duality; H control; Optimization methods; Robustness; State space methods; Uncertainty

Indexed keywords

CONSTRAINT THEORY; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); STATE SPACE METHODS; UNCERTAIN SYSTEMS;

LINEAR MATRIX INEQUALITIES;

CONTROL SYSTEM SYNTHESIS;

EID: 0032685972     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.769369     Document Type: Article

References (26)

1. M. G. Safonov and M. Athans, "A multiloop generalization of the circle criterion for stability margin analysis," IEEE Trans. Automat. Contr., vol. 26, pp. 415-422, 1981.
2. A. Packard and J. C. Doyle, "The complex structured singular value," Automatica, vol. 29, no. 1, pp. 71-109, 1993.
3. A. Rantzer and A. Megretskii, "System analysis via integral quadratic constraints," in Proc. IEEE Conf. Decision and Contol, 1994, pp. 3062-3067.
4. K. C. Goh and M. G. Safonov, "Robust analysis, sectors, and quadratic functionals," in Proc. IEEE Conf. Decision and Control, 1995, pp. 1988-1993.
5. O. Toker and H. Ozbay, "On the NP-hardness of solving bilinear matrix inequalities and the simultaneous stabilization with static output feedback," in Proc. American Control Conf., 1995, pp. 2525-2526.
6. J. C. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, "State-space solutions to standard H2 and H-infinity control problems," IEEE Trans. Automat. Contr., vol. 34, pp. 831-847, Aug. 1989.
7. P. Gahinet and P. Apkarian, "A linear matrix inequality approach to H-infinity control," Int. J. Robust and Nonlinear Contr., vol. 4, pp. 421-448, 1994.
8. A. Packard, "Gain scheduling via linear fractional transformations," Syst. Contr. Lett., vol. 22, no. 2, pp. 79-92, 1994.
9. M. A. Dahleh and I. J. Diaz-Bobillo, Control of Uncertain Systems. Englewood Cliffs, NJ: Prentice-Hall, 1995.
10. B. Kouvaritakis and H. Latchman, "Necessary and sufficient stability criterion for systems with structured uncertainty: The major principle direction alignment principle," Int. J. Contr., vol. 42, pp. 575-598, 1985.
11. P. M. Young, "Robustness analysis with full-structured uncertainties," in Proc. IEEE Conf. Decision and Contr., 1996, pp. 3464-3469.
12. R. D' Andrea, "H-infinity optimization with spatial constraints," in Proc. IEEE Conf. Decision and Control, 1995, pp. 4327-4332.
13. F. Paganini, "A set-based approach for white noise modeling," IEEE Trans. Automat. Contr., vol. 41, pp. 1453-1455, Oct. 1996.
14. F. Paganini, R. D'Andrea, and J. C. Doyle, "Behavioral approach to robustness analysis," in Proc. American Control Conf., 1994, pp. 2782-2786.
15. F. Paganini, "Necessary and sufficient conditions for robust H-2 performance," in Proc. IEEE Conf. Decision and Control, 1995, pp. 1970-1975.
16. J. C. Doyle, K. M. Zhou, K. Glover, and B. Bodenheimer, "Mixed H2 and H-infinity performance objectives II: Optimal control," IEEE Trans. Automat. Contr., vol. 39, pp. 1575-1587, Aug. 1994.
17. R. D'Andrea, "LMI approach to mixed H-2 and H-infinity performance objective controller design," in Proc. IFAC World Congr., 1996, vol. G, pp. 327-332.
18. _, "Generalized l-2 synthesis with dynamic constraints," Math. Theory of Networks and Syst., 1998.
19. A. Megretski and S. Treil, "Power distribution inequalities in optimization and robustness of uncertain systems," J. Math. Syst., Estimation and Contr., vol. 3, no. 3, pp. 301-319, Mar. 1993.
20. V. A. Yakubovich, "S-procedure in nonlinear control theory," Vestnik Leningrad Univ.: Mathematics, pp. 62-77, 1971 (in Russian).
21. F. Paganini, "Sets and constraints in the analysis of uncertain systems," Ph.D. dissertation, California Institute of Technol., 1995.
22. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
23. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1994.
24. R. D'Andrea, "Controller synthesis for plants subject to linear time invariant full structured uncertainty," in Proc. IEEE Conf. Decision and Control, 1997, pp. 2708-2713.
25. _, "Necessary and sufficient conditions for gain scheduling subject to full-structured uncertainty," in Proc. IEEE Conf. Decision and Control, 1996, pp. 3760-3765.
26. R. T. Rockafellar, Convex Analysis. Princeton, NJ: Princeton Univ. Press, 1970.