A global high-gain finite-time observer

IEEE Transactions on Automatic Control

Volumn 55, Issue 6, 2010, Pages 1500-1506

  Ménard, Tomas ^a   Moulay, Emmanuel ^b   Perruquetti, Wilfrid ^c,d  

^a INSTITUT DE RECHERCHE EN COMMUNICATIONS ET CYBERNÉTIQUE DE NANTES   (France)

^b UNIVERSITÉ DE POITIERS   (France)

^c INRIA   (France)

^d ECOLE CENTRALE DE LILLE   (France)

Author keywords

Finite time observer; Finite time stability; Uniformly observable

Indexed keywords

FINITE TIME STABILITY; HIGH-GAIN; LIPSCHITZ;

LYAPUNOV FUNCTIONS;

SYSTEM STABILITY;

EID: 77953089632     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2045698     Document Type: Article

References (33)

1. A. Azemi and E. E. Yaz, "Sliding-mode adaptive observer approach to chaotic synchronization," J. Dyn. Syst., Meas., Control, vol.122, pp. 758-765, 2000.
2. A. Bacciotti and L. Rosier, Lyapunov Functions and Stability in Control Theory, 2nd ed. New York: Springer, 2005.
3. G. Besancon, Nonlinear Observers and Applications. New York: Springer Verlag, 2007.
4. S. P. Bhat and D. S. Bernstein, "Finite-time stability of continuous autonomous systems," SIAM J. Control Optim., vol.38, no.3, pp. 751-766, 2000.
5. S. P. Bhat and D. S. Bernstein, "Geometric homogeneity with applications to finite-time stability," Math. Control, Signals Syst., vol.17, pp. 101-127, 2005.
6. G. Conte, C. H. Moog, and A. M. Perdon, Algrebraic Methods for Nonlinear Control Systems, 2nd ed. New York: Springer, 2007.
7. S. V. Drakunov and V. I. Utkin, "Sliding mode observers. tutorial," in Proc. 34th IEEE Conf. Decision Control, 1995, pp. 3376-3378.
8. R. Engel and G. Kreisselmeier, "A continuous-time observer which converges in finite-time," IEEE Trans. Autom. Control, vol.47, no.7, pp. 1202-1204, Jul. 2002.
9. T. Floquet and J. P. Barbot, "Super twisting algorithm based step-bystep sliding mode observers for nonlinear systems with unknown inputs," Special Issue IJSS Adv. Sliding Mode Observation Estim., vol.38, no.10, pp. 803-813, Jan. 2008.
10. T. Floquet, J. P. Barbot, W. Perruquetti, and M. Djemai, "On the robust fault detection via sliding mode perturbation observer," Int. J. Control, vol.77, no.7, pp. 622-629, 2004.
11. J. P. 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.
12. J. P. Gauthier and I. A. K. Kupka, "Observability and observers for nonlinear systems," SIAM J. Control Optim., vol.32, pp. 975-994, 1994.
13. A. Glumineau, C. H. Moog, and F. Plestan, "New algebro-geometric conditions for the linearization by input-output injection," IEEE Trans. Autom. Control, vol.40, no.4, pp. 598-603, Apr. 1996.
14. H. Hammouri, B. Targui, and F. Armanet, "High gain observer based on a triangular structure," Int. J. Robust Nonlin. Struct., vol.12, no.6, pp. 497-518, 2002.
15. I. Haskara, U. Ozguner, and V. Utkin, "On sliding mode observers via equivalent control approach," Int. J. Control, vol.71, pp. 1051-1067, 1998.
16. Y. Hong, Y. Xu, and J. Huang, "Finite-time control for robot manipulators," Syst. Control Lett., vol.46, no.4, pp. 243-253, 2002.
17. N. Kazantzis and C. Kravaris, "Nonlinear observer design using lyapunov's auxiliary theorem," Syst. Control Lett., vol.34, pp. 241-247, 1998.
18. H. K. Khalil, Nonlinear Systems. Englewood Cliffs, NJ: Prentice- Hall, 1996.
19. A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM J. Control Optim., vol.23, no.2, pp. 197-216, 1985.
20. J. Li and C. Qian, "Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems," IEEE Trans. Automatic Control, vol.51, no.5, pp. 879-884, May 2006. (Pubitemid 43792657)
21. P. H. Menold, R. Findeisen, and F. Allgöwer, "Finite-time convergent observers for linear time varying systems," in Proc. 11th Mediterranean Conf. Control Autom., 2003, [CD ROM].
22. H. Michalska and D. Mayne, "Moving horizon observers and observer- based control," IEEE Trans. Autom. Control, vol.40, no.6, pp. 995-1006, Jun. 1995.
23. E. Moulay and W. Perruquetti, "Finite-time stability of nonlinear systems," in Proc. 42th IEEE Conf. Decision Control, Maui, HI, Dec. 2003, pp. 3641-3646.
24. E. Moulay and W. Perruquetti, "Finite time stability of differential inclusions," IMA J. Math. Control Inform, vol.22, no.4, pp. 465-475, 2005.
25. E. Moulay and W. Perruquetti, "Finite time stability and stabilization of a class of continuous systems," J. Math. Anal. Appl., vol.323, no.2, pp. 1430-1443, 2006.
26. E. Moulay and W. Perruquetti, "Finite-time stability conditions for non-autonomous continuous systems," Int. J. Control, vol.81, no.5, pp. 797-803, 2008. (Pubitemid 351502920)
27. W. Perruquetti and S. Drakunov, "Finite time stability and stabilisation," in Proc. IEEE Conf. Decision Control, Sydney, Australia, 2000, pp. 1894-1899.
28. W. Perruquetti, T. Floquet, and E. Moulay, "Finite-time observers: Application to secure communication," IEEE Trans. Autom. Control, vol.53, no.1, pp. 356-360, Feb. 2008.
29. F. Plestan, J. W. Grizzle, E. R. Westervelt, and G. Abba, "Stable walking of a 7-dof biped robot," IEEE Trans. Robot. Autom., vol.19, no.4, pp. 653-668, Apr. 2003.
30. F. Sauvage, M. Guay, and D. Dochain, "Design of a nonlinear finitetime converging observer for a class of nonlinear systems," J. Control Sci. Eng. 2007 [Online]. Available: http://www.hindawi.com/journals/ jcse/2007/036954.abs.html
31. Y. Shen, W. Shen, M. Jiang, and Y. Huang, "Semi-global finite-time observers for multi-output nonlinear systems," Int. J. Robust Nonlin. Control, vol.20, no.7, pp. 789-801, 2009.
32. Y. Shen and X. Xia, "Semi-global finite-time observers for nonlinear systems," Automatica, vol.44, no.12, pp. 3152-3156, 2008.
33. M. C. Young and R. Rajamani, "A systematic approach to adaptive observer synthesis for nonlinear systems," IEEE Trans. Autom. Control, vol.42, no.4, pp. 534-537, Apr. 1997