Control design for bilinear systems with a guaranteed region of stability: An LMI-based approach

2009 17th Mediterranean Conference on Control and Automation, MED 2009

Volumn 2009-January, Issue , 2009, Pages 809-814

  Tarbouriech, S ^a   Queinnec, I ^a   Calliero, T R ^b   Peres, P L D ^c  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b LAAS CNRS   (France)

^c UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED LOOP SYSTEMS; CONVEX OPTIMIZATION; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK CONTROL; STATE FEEDBACK;

BILINEAR SYSTEM; CONSTRUCTIVE CONDITIONS; CONTROL DESIGN; CONVEX OPTIMIZATION PROBLEMS; LMI-BASED APPROACH; REGION OF STABILITIES; STABILITY CONDITION; STABILIZING STATE;

SYSTEM STABILITY;

EID: 85038812995     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MED.2009.5164643     Document Type: Conference Paper

References (34)

1. R. R. Mohler, Bilinear control process. New York, USA: Academic Press, 1973.
2. R. R. Mohler and W. J. Kolodziej, "An overview of bilinear system theory and applications," IEEE Trans. Syst., Man, and Cybern., vol. 10, no. 10, pp. 683-688, October 1980.
3. R. Longchamp, "Controller design for bilinear systems," IEEE Trans. Automat. Contr., vol. 25, no. 3, pp. 547-548, 1980.
4. P. O. Gutman, "Stabilizing controllers for bilinear systems," IEEE Trans. Automat. Contr., vol. 26, no. 4, pp. 917-922, April 1981.
5. D. E. Koditschek and K. S. Narendra, "Stabilizability of second-order bilinear systems," IEEE Trans. Automat. Contr., vol. 28, no. 10, pp. 987-989, October 1983.
6. E. P. Ryan and N. J. Buckingham, "On asymptotically stabilizing feedback control of bilinear systems," IEEE Trans. Automat. Contr., vol. 28, no. 8, pp. 863-864, August 1983.
7. R. Genesio and A. Tesi, "The output stabilization of SISO bilinear systems," IEEE Trans. Automat. Contr., vol. 33, no. 10, pp. 950-952, October 1988.
8. R. Luesink and H. Nijmeijer, "On the stabilization of bilinear systems via constant feedback," Lin. Alg. Appl., vol. 122-124, pp. 457-474, September-November 1989.
9. L. K. Chen, X. Yang, and R. R. Mohler, "Stability analysis of bilinear systems," IEEE Trans. Automat. Contr., vol. 36, no. 11, pp. 1310-1315, November 1991.
10. M. S. Chen and S. T. Tsao, "Exponential stabilization of a class of unstable for bilinear systems," IEEE Trans. Automat. Contr., vol. 45, no. 5, pp. 989-992, May 2000.
11. S. Sasaki and K. Uchida, "Quadratic cost output feedback control for bilinear systems," Int. J. Syst. Sci., vol. 34, no. 5, pp. 345-355, April 2003.
12. M. S. Chen, "Exponential stabilization of constrained bilinear systems," Automatica, vol. 34, no. 8, pp. 989-992, August 1998.
13. M. Bacic, M. Cannon, and B. Kouvaritakis, "Constrained control of SISO bilinear systems," IEEE Trans. Automat. Contr., vol. 48, no. 8, pp. 1443-1447, August 2003.
14. M. Frayman, "On the relationship between bilinear and quadratic systems," IEEE Trans. Automat. Contr., vol. 20, no. 4, pp. 567-568, August 1975.
15. H.-D. Chiang, M. W. Hirsch, and F. F. Wu, "Stability regions of nonlinear autonomous dynamical systems," IEEE Trans. Automat. Contr., vol. 33, no. 1, pp. 16-27, January 1988.
16. H.-D. Chiang and J. S. Thorp, "Stability regions of nonlinear dynamical systems: a constructive methodology," IEEE Trans. Automat. Contr., vol. 34, no. 12, pp. 1229-1241, December 1989.
17. A. Tesi, F. Villoresi, and R. Genesio, "On the stability domain estimation via a quadratic Lyapunov function: convexity and optimality properties for polynomial systems," IEEE Trans. Automat. Contr., vol. 41, no. 11, pp. 1650-1657, 1996.
18. G. Chesi, A. Tesi, A. Vicino, and R. Genesio, "On convexification of some minimum distance problems," in Proc. 5th Eur. Control Conf., Karlsruhe, Germany, August 1999
19. B. Tibken, "Estimation of the domain of attraction for polynomial systems via LMI's," in Proc. 39th IEEE Conf. Decision Contr., Sydney, Australia, December 2000, pp. 3860-3865.
20. B. Tibken and. Hachicho, "Estimation of the domain of attraction for polynomial systems using multidimensional grid," in Proc. 39th IEEE Conf. Decision Contr., Sydney, Australia, December 2000, pp. 3870-3874.
21. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Solving quadratic distance problems: An LMI-based approach," IEEE Trans. Automat. Contr., vol. 48, no. 2, pp. 200-212, February 2003.
22. G. Chesi, "Estimating the domain of attraction for uncertain polynomial systems," Automatica, vol. 40, no. 11, pp. 1981-1986, November 2004.
23. -, "Computing output feedback controllers to enlarge the domain of attraction in polynomial systems," IEEE Trans. Automat. Contr., vol. 49, no. 10, pp. 1846-1850, October 2004.
24. F. Amato, C. Cosentino, and A. Merola, "On the region of attraction of nonlinear quadratic systems," Automatica, vol. 43, no. 12, pp. 2119-2123, December 2007.
25. I. Derese and E. Noldus, "Design of linear feedback laws for bilinear systems," Int. J. Contr., vol. 31, no. 2, pp. 219-237, 1980.
26. F. Amato, C. Cosentino, and A. Merola, "Stabilization of bilinear systems via linear state feedback control," in Proc. 15th Medit. Conf. Contr. Aut. (MED2007), Athens, Greece, 2007.
27. 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.
28. V. Mahout, S. Tarbouriech, and G. Garcia, "Controller design for unstable uncertain bilinear systems," in Proc. 10th Medit. Conf. Contr. Aut. (MED2002), Lisbon, Portugal, July 2002, cD-rom.
29. H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice Hall, 1996.
30. F. Amato, R. Ambrosino, M. Ariola, C. Cosentino, and A. Merola, "State feedback control of nonlinear quadratic systems," in Proc. 46th IEEE Conf. Decision Contr., New Orleans, LA, December 2007, pp. 1699-1703.
31. V. F. Montagner, R. C. L. F. Oliveira, P. L. D. Peres, S. Tarbouriech, and I. Queinnec, "Gain-scheduled controllers for linear parametervarying systems with saturating actuators: LMI-based design," in Proc. 2007 Amer. Control Conf., New York, NY, USA, July 2007, pp. 6067-6072.
32. V. Kapila and K. M. Grigoriadis, Eds., Actuator Saturation Control, ser. Control Engineering Series. New York, NY: Marcel Dekker, Inc., 2002.
33. S. Tarbouriech, G. Garcia, and A. H. Glattfelder, Eds., Advanced Strategies in Control Systems with Input and Output Constraints, ser. Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer-Verlag, 2007, vol. 346.
34. S. Tarbouriech, C. Prieur, and J. M. Gomes da Silva Jr., "Stability analysis and stabilization of systems presenting nested saturations," IEEE Trans. Automat. Contr., vol. 51, no. 8, pp. 1364-1371, August 2006.