Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions

IEEE Transactions on Automatic Control

Volumn 41, Issue 7, 1996, Pages 1041-1046

  Feron, Eric ^a   Apkarian, Pierre ^b   Gahinet, Pascal ^c  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b Centre d'Etudes et de Recherches en Psychopathologie   (France)

^c INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM SYNTHESIS; FREQUENCY DOMAIN ANALYSIS; LYAPUNOV METHODS; MATRIX ALGEBRA; NUMERICAL METHODS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY;

PARAMETER UNCERTAINTY; POPOV STABILITY;

CONTROL SYSTEM ANALYSIS;

EID: 0030195747     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.508913     Document Type: Article

References (24)

1. R. S. Adams and S. S. Banda, "Robust flight control design using dynamic inversion and structured singular value synthesis," IEEE Trans. Circuits Syst., vol. 1, no. 2, pp. 80-92, June 1993.
2. P. Apkarian, E. Feron, and P. Gahinet, "Parameter-dependent Lyapunov functions for robust control of systems with real parametric uncertainty," in Proc. European Contr. Conf., Roma, Italy, Sept. 1995, pp. 2275-2280.
3. G. J. Balas, J. Reiner, and W. Garrard, "Design of flight control system for a highly maneuverable aircraft using μ synthesis," in Proc. AIAA Guid. Contr. Conf., Monterey, CA, 1993.
4. B. R. Barmish, "Stabilization of uncertain systems via linear control," IEEE Trans. Automat. Contr., vol. AC-27, no. 8, pp. 84-8-850, Oct. 1982.
5. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," SIAM Studies Appl. Math., SIAM, vol. 15, 1994.
6. F. M. Callier and C. A. Desoer, Multivariable Feedback Systems. New York: Springer-Verlag, 1982.
7. C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York: Academic, 1975.
8. J. C. Doyle, K. Lenz, and A. Packard, "Design examples using μ-synthesis: Space shuttle lateral axis FCS during reentry," in Proc. IEEE Conf. Decision Contr., Athens, Greece, 1986, pp. 2218-2223.
9. J. C. Doyle, A. Packard, and K. Zhou, "Review of LFT's, LMI's and μ," in Proc. IEEE Corf. Decision Contr., Brighton, England, 1991, pp. 1227-1232.
10. M. K. H. Fan, A. L. Tits, and J. C. Doyle, "Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics," IEEE Trans. Automat. Contr., vol. 36, no. 1, pp. 25-38, Jan. 1991.
11. E. Feron, P. Apkarian, and P. Gahinet, "S-procedure for the analysis of control systems with parametric uncertainties via parameter-dependent Lyapunov functions," in Proc. European Contr. Conf., Roma, Italy, Sept. 1995, pp. 141-146.
12. A. L. Fradkov and V. A. Yakubovich, "The S-procedure and duality relations in nonconvex problems of quadratic programming," Vestnik Leningrad Univ. Math., vol. 6, no. 1, pp. 101-109, 1979; in Russian, 1973.
13. ∞ control," Int. J. Robust Nonl. Contr., vol. 4, no. 4, pp. 421-448, 1994.
14. P. Gahinet, P. Apkarian, and M. Chilali, "Parameter-dependent Lyapunov functions for real parametric uncertainty," IEEE Trans. Automat. Contr., vol. 41, no. 3, pp. 436-442, 1996.
15. P. Gahinet, A. Nemirovskii, A. J. Laub, and M. Chilali, LMI Control Toolbox. The MathWorks, 1994, 1995.
16. W. Haddad and D. Bernstein, "Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part I: Continuous time theory," Int. J. Robust Nonlinear Contr., vol. 3, pp. 313-339, 1993.
17. A. M. Lyapunov, "Problème général de la stabilité du mouvement," Annals of Mathematics Studies, vol. 17. Princeton, NJ: Princeton Univ. Press, 1947.
18. J. C. Morris, P. Apkarian, and J. C Doyle, "Synthesizing robust mode shapes with μ and implicit model following," in Proc. IEEE Conf. Contr. Appl., Dayton, Ohio, Sept. 1992.
19. K. S. Narendra and J. H. Taylor, "Frequency domain criteria for absolute stability," Electrical Science. New York: Academic, 1973.
20. J. C. Willems, "Least squares stationary optimal control and the algebraic Riccati equation," IEEE Trans. Automat. Contr., vol. AC-16, no. 6, pp. 621-634, Dec. 1971.
21. ∞ optimal control with μ-synthesis," in Proc. Amer. Contr. Conf., May 1990, pp. 2362-2367.
22. V. A. Yakubovich, "The S-procedure in nonlinear control theory," Vestnik Leningrad Univ. Math., vol. 4, pp. 73-93, 1977; in Russian, 1971.
23. P. M. Young, "Robustness with parametric and dynamic uncertainty," Ph.D. dissertation, California Inst. Technol., 1993.
24. K. Zhou and P. P. Khargonekar, "On the stabilization of uncertain linear systems via bound invariant Lyapunov functions," SIAM J. Contr. Optimiz., vol. 26, pp. 1265-1273, 1988.