H∞ filter for bilinear systems using LPV approach

IEEE Transactions on Automatic Control

Volumn 55, Issue 7, 2010, Pages 1668-1674

  Gérard, Benjamin ^a   Souley Ali, Harouna ^b   Zasadzinski, Michel ^b   Darouach, Mohamed ^b  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

^b CENTRE DE RECHERCHE EN AUTOMATIQUE DE NANCY   (France)

Author keywords

Bilinear systems; functional filter; H performance; high gain filter; linear parameter varying (LPV) approach; observability

Indexed keywords

BILINEAR SYSTEM; FUNCTIONAL FILTERS; HIGH GAIN; HIGH GAIN FILTER; LINEAR PARAMETER VARYING;

CONVEX OPTIMIZATION; DESIGN; DISCRETE TIME CONTROL SYSTEMS; MATRIX ALGEBRA;

OBSERVABILITY;

EID: 77954550473     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2046075     Document Type: Article

References (28)

1. W. Rugh, "Nonlinear system theory," in Johns Hopkins Series in Information Sciences and Systems. Baltimore, MD: Johns Hopkins Univ. Press, 1981.
2. R. Mohler, Nonlinear Systems: Applications to Bilinear Control. Englewood Cliffs, NJ: Prentice Hall, 1991, vol.2.
3. D. Williamson, "Observation of bilinear systems with application to biological control," Automatica, vol.13, pp. 243-254, 1977.
4. S. Hara and K. Furuta, "Minimal order state observers for bilinear systems," Int. J. Control, vol.24, pp. 705-718, 1976.
5. O. Grasselli and A. Isidori, "An existence theorem for observers of bilinear systems," IEEE Trans. Autom. Control, vol.AC-26, no.6, pp. 1299-1300, Dec. 1981.
6. M. Zasadzinski, H. Rafaralahy, C. Mechmeche, and M. Darouach, "On disturbance decoupled observer for a class of bilinear systems," Trans. ASME, J. Dyn. Syst., Meas., Control, vol.120, pp. 371-377, 1998.
7. M. Darouach, M. Zasadzinski, and M. Hayar, "Reduced-order observer design for descriptor systems with unknown inputs," IEEE Trans. Autom. Control, vol.41, no.7, pp. 1068-1072, Jul. 1996.
8. G. Bornard, N. Couenne, and F. Celle, "Regularly persistent observers for bilinear systems," in New Trends in Nonlinear Control Theory, ser. Lecture Notes in Control and Information Sciences, J. Descusse, M. Fliess, A. Isidori, and D. Leborgne, Eds. New York: Springer-Verlag, 1988, vol.122, pp. 130-140.
9. J. Gauthier, H. Hammouri, and S. Othman, "A simple observer for nonlinear systems, applications to bioreactors," IEEE Trans. Autom. Control, vol.37, no.6, pp. 875-880, Jun. 1992.
10. K. Busawon and J. De Leon-Morales, "An improved high gain observer for single input uniformly observable systems," in Proc. Eur. Control Conf., Karlsruhe, Germany, 1999, [CD ROM].
11. M. Rodrigues, H. Hammouri, C. Mechmeche, and N. B. Braiek, "A high gain observer based LMI approach," in Proc. Triennal IFACWorld Congress, Seoul, Korea, 2008, pp. 2803-2807.
12. I. Derese, P. Stevens, and E. Noldus, "Observers for bilinear systems with bounded input," Int. J. Syst. Sci., vol.10, pp. 649-668, 1979.
13. B. Tibken and E. Hofer, "Systematic observer design for bilinear systems," in Proc. IEEE Int. Sympo. Circuits Syst, Portland, OR, 1989, pp. 1611-1616.
14. W. Wang and C. Kao, "Estimator design for bilinear systems with bounded inputs," J. Chinese Inst. Eng., vol.14, pp. 157-163, 1991.
15. S. Raghavan and J. Hedrick, "Observer design for a class of nonlinear systems," Int. J. Control, vol.59, pp. 515-528, 1994.
16. R. Rajamani, "Observer for lipschitz nonlinear systems," IEEE Trans. Autom. Control, vol.43, no.3, pp. 397-401, Mar. 1998.
17. H. S. Ali, M. Zasadzinski, H. Rafaralahy, and M. Darouach, "Robust H∞ reduced order functional filtering for uncertain bilinear systems," Automatica, vol.42, pp. 405-413, 2006.
18. R. Hermann and A. Krener, "Nonlinear controllability and observability," IEEE Trans. Autom. Control, vol.22, no.5, pp. 728-740, Oct. 1977.
19. B. Gérard, H. S. Ali, M. Zasadzinski, and M. Darouach, "LPV approach for H∞ reduced order filters for bilinear systems," in Proc. Eur. Control Conf., Kos, Greece, 2007, [CD ROM].
20. C. Rao and S. Mitra, Generalized Inverse of Matrices and its Applications. New York: Wiley, 1971.
21. 2 -gain analysis of nonlinear systems and nonlinear state-feedbackH∞ control," IEEE Trans. Autom. Control, vol.37, no.6, pp. 770-784, Jun. 1992.
22. E. Fridman and U. Shaked, "A descriptor system approach toH∞ control of linear time-delay systems," IEEE Trans. Autom. Control, vol.47, no.2, pp. 253-270, Feb. 2002.
23. S. Chughtai and N. Munro, "LMI-based gain-scheduled control," in Proc. Control Conf. Congress, Bath, U.K., 2004, no.009, [CD ROM].
24. M. Seron, J. Braslavsky, and G. Goodwin, Fundamental Limitations in Filtering and Control. New York: Springer-Verlag, 1997.
25. M. Darouach, "Existence and design of functional observers for linear systems," IEEE Trans. Autom. Control, vol.45, no.5, pp. 940-943, May 2000.
26. P. Apkarian, P. Gahinet, and J. Biannic, "Affine parameter-dependent Lyapunov functions for real parametric uncertainty," in Proc. IEEE Conf. Decision Control, Lake Buena Vista, FL, 1994, pp. 2026-2031.
27. F. Deza, E. Busvelle, J. Gauthier, and D. Rakotopara, "High gain estimation for nonlinear systems," Syst. Control Lett., vol.18, pp. 295-299, 1992.
28. F. Deza, D. Bossanne, E. Busvelle, J. Gauthier, and D. Rakotopara, "Exponential observers for nonlinear systems," IEEE Trans. Autom. Control, vol.38, no.3, pp. 482-484, Mar. 1993.