State feedback gain scheduling for linear systems with time-varying parameters

Proceedings of the American Control Conference

Volumn 3, Issue , 2004, Pages 2004-2009

  Montagner, Vinícius F ^a   Peres, Pedro L D ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

MULTICONVEXITY; QUADRATIC FUCTIONS; QUADRATIC STABILIZABILITY;

FUNCTIONS; LINEAR SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; PARAMETER ESTIMATION; ROBUSTNESS (CONTROL SYSTEMS);

FEEDBACK CONTROL;

EID: 8744276300     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2004.182396     Document Type: Conference Paper

References (27)

1. D. J. Leith and W. E. Leithead, "Survey of gain-scheduling analysis and design," Int. J. Contr., vol. 73, no. 11, pp. 1001-1025, July 2000.
2. W. J. Rugh and J. S. Shamma, "Research on gain scheduling," Automatica, vol. 36, no. 10, pp. 1401-1425, October 2000.
3. D. J. Stilwell and W. J. Rugh, "Interpolation of observer state feedback controllers for gain scheduling," IEEE Trans. Automat. Contr., vol. 44, no. 6, pp. 1225-1229, June 1999.
4. J. S. Shamma and M. Athans, "Guaranteed properties of gain scheduled control for linear parameter-varying plants," Automatica, vol. 27, no. 3, pp. 559-564, 1991.
5. _, "Gain scheduling: potential hazards and possible remedies," IEEE Control Syst. Mag., vol. 12, no. 3, pp. 101-107, June 1992.
6. J. Bernussou, P. L. D. Peres, and J. C. Geromel, "A linear programming oriented procedure for quadratic stabilization of uncertain systems," Syst. Contr. Lett., vol. 13, no. 1, pp. 65-72, July 1989.
7. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM Studies in Applied Mathematics, 1994.
8. M. Johansson, Piecewise Linear Control Systems - A Computational Approach, ser. Lecture Notes in Control and Information Science. Heidelberg, Germany: Springer-Verlag, 2003, vol. 284.
9. J. C. Geromel, M. C. de Oliveira, and L. Hsu, "LMI characterization of structural and robust stability," Lin. Alg. Appl., vol. 285, no. 1-3, pp. 69-80, December 1998.
10. D. C. W. Ramos and P. L. D. Peres, "An LMI condition for the robust stability of uncertain continuous-time linear systems," IEEE Trans. Automat. Contr., vol. 47, no. 4, pp. 675-678, April 2002.
11. V. J. S. Leite and P. L. D. Peres, "An improved LMI condition for robust D-stability of uncertain polytopic systems," IEEE Trans. Automat. Contr., vol. 48, no. 3, pp. 500-504, March 2003.
12. F. Amato, M. Corless, M. Mattei, and R. Setola, "A multivariable stability margin in the presence of time-varying, bounded rate gains," Int. J. Robust Nonlinear Contr., vol. 7, pp. 127-143, 1997.
13. E. Feron, P. Apkarian, and P. Cabinet, "Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions," IEEE Trans. Automat. Contr., vol. 41, no. 7, pp. 1041-1046, July 1996.
14. P. Gahinet, P. Apkarian, and M. Chilali, "Affine parameter-dependent Lyapunov functions and real parametric uncertainty," IEEE Trans. Automat. Contr., vol. 41, no. 3, pp. 436-442, March 1996.
15. W. M. Haddad and D. S. Bernstein, "Parameter-dependent Lyapunov functions and the Popov Criterion in robust analysis and synthesis," IEEE Trans. Automat. Contr., vol. 40, no. 3, pp. 536-543, 1995.
16. P. Apkarian and H. D. Tuan, "Parametrized LMIs in control theory," SIAM J. Control Optim., vol. 38, no. 4, pp. 1241-1264, May 2000.
17. F. Wang and V. Balakrishnan, "Improved stability analysis and gain-scheduled controller synthesis for parameter-dependent systems," IEEE Trans. Automat. Contr., vol. 47, no. 5, pp. 720-734, May 2002.
18. P. Apkarian and R. J. Adams, "Advanced gain-scheduling techniques for uncertain systems," IEEE Trans. Trans. Contr. Syst. Technol., vol. 6, no. 1, pp. 21-32, 1998.
19. F. Wu, "A generalized LPV system analysis and control synthesis framework," Int. J. Contr., vol. 74, no. 7, pp. 745-759, May 2001.
20. 2-norm control for LPV systems with bounded parameter variation rates," Int. J. Robust Nonlinear Contr., vol. 6, pp. 983-998, 1996.
21. P. Apkarian and P. Gahinet, "A convex characterization of gainscheduled ℋ∞ controllers," IEEE Trans. Automat. Contr., vol. 40, no. 5, pp. 853-864, May 1995.
22. A. Packard, "Gain scheduling via linear fractional transformations," Syst. Contr. Lett., vol. 22, no. 2, pp. 79-92, February 1994.
23. G. Scorletti and L. E. Ghaoui, "Improved LMI conditions for gain scheduling and related control problems," Int. J. Robust Nonlinear Contr., vol. 8, no. 10, pp. 845-877, August 1998.
24. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox for use with Matlab. The Math Works Inc.: User's Guide, 1995.
25. V. F. Montagner and P. L. D. Peres, "A new LMI condition for the robust stability of linear time-varying systems," in Proc. 42nd IEEE Conf. Decision Contr., Maui, HI, USA, December 2003, pp. 6133-6138.
26. P. L. D. Peres and J. C. Geromel, "An alternate numerical solution to the linear quadratic problem," IEEE Trans. Automat. Contr., vol. 39, no. 1, pp. 198-202, January 1994.
27. V. J. S. Leite, V. F. Montagner, and P. L. D. Peres, "Robust pole location by parameter dependent state feedback control," in Proc. 41st IEEE Conf. Decision Contr., Las Vegas, December 2002, pp. 1864-1869.