On the "uniform" observability of discrete-time nonlinear systems

IEEE Transactions on Automatic Control

Volumn 54, Issue 8, 2009, Pages 1925-1928

  Hanba, Shigeru ^a  

^a UNIVERSITY OF THE RYUKYUS   (Japan)

Author keywords

Discrete time nonlinear system

Indexed keywords

COMPACT SETS; DISCRETE-TIME NONLINEAR SYSTEM; DISCRETE-TIME NONLINEAR SYSTEMS; INITIAL STATE; NONUNIFORM; OBSERVATION WINDOW; TECHNICAL NOTES;

CONTINUOUS TIME SYSTEMS; OBSERVABILITY;

NONLINEAR SYSTEMS;

EID: 68949186428     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2023775     Document Type: Article

References (34)

1. M. Alamir and L. A. Calvillo-Corona, "Further results on nonlinear receding-horizon observers," IEEE Trans. Automat. Control, vol. 47, no. 7, pp. 1184-1188, Jul. 2002.
2. F. Albertini and D. D'Alessandro, "Observability and forward-backward observability of discrete-time nonlinear systems," Math. Control, Signals, Syst., vol. 15, no. 4, pp. 275-290, 2002.
3. A. Alessandri, M. Baglietto, and G. Battistelli, "Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation scheme," Automatica, vol. 44, no. 7, pp. 1753-1765, 2008.
4. S. Benamorl, H. Hammouri, and F. Couenne, "A luenberger-like observer for discrete-time nonlinear systems," in Proc. 37th IEEE Conf. Decision Control, Tampa, FL, 1998, pp. 4612-4613.
5. G. Besançon, H. Hammouri, and S. Benamor, "State equivalence of discrete-time nonlinear control systems to state affine form up to input/output injection," Syst. Control Lett., vol. 33, no. 1, pp. 1-10, 1998.
6. G. Besançon and H. Hammouri, "Some remarks on dynamic output feedback control of non uniformly observable systems," in Proc. 39th IEEE Conf. Decision Control, Sydney, Australia, 2000, pp. 2462-2465.
7. G. Besançon, "An overview on observer tools for nonlinear systems," in Nonlinear Observers and Applications, G. Besançon, Ed. Berlin, Heidelberg, Germany: Springer-Verlag, 2007, pp. 1-33.
8. G. Besançon and A. Ticlea, "An immersion-based observer design for rank-observable nonlinear systems," IEEE Trans. Automat. Control, vol. 52, no. 1, pp. 83-88, Jan. 2007.
9. E. Busvelle and J.-P. Gauthier, "Observation and identification tools for nonlinear systems: Application to a fluid catalytic cracker," in Int. J. Control, vol. 78, no. 3, pp. 208-234, 2005.
10. C. Califano, S. Monaco, and D. Normand-Cyrot, "On the observer design in discrete-time," Syst. Control Lett., vol. 49, no. 4, pp. 255-265, 2003.
11. R. Findeisen, L. Imsland, F. Allgöwer, and B. A. Foss, "Output feedback stabilization of constrained systems with nonlinear predictive control," in Int. J. Robust Nonlin. Control, vol. 13, no. 3-4, pp. 211-227, 2003.
12. J. M. Fitts, "On the observability of non-linear systems with applications to non-linear regression analysis," in Inform. Sci., vol. 4, no. 3, pp. 129-156, 1972.
13. J. P. Gauthier, H. Hammouri, and S. Othman, "A simple observer for nonlinear systems applications to bioreactors," IEEE Trans. Automat. Control, vol. 37, no. 6, pp. 875-880, Jun. 1992.
14. H. Hammouri, "Uniform observability and observer synthesis," in Nonlinear Observers and Applications, G. Besançon, Ed. Berlin, Heidelberg, Germany: Springer-Verlag, 2007, pp. 35-70.
15. A. Isidori, Nonlinear Control Systems, 3rd ed. London, U.K.: Springer-Verlag, 1995.
16. ∞ observability of single-input C ∞-systems," J. Dyn. Control Syst., vol. 7, no. 2, pp. 151-169, 2001.
17. I. Karafyllis and C. Kravaris, "On the observer problem for discrete-time control systems," IEEE Trans. Automat. Control, vol. 52, no. 1, pp. 12-25, Jan. 2007.
18. H. Keller, "Non-linear observer design by transformation into a generalized observer canonical form," in Int. J. Control, vol. 46, no. 6, pp. 1915-1930, 1987.
19. G. Kreisselmeier and R. Engel, "Nonlinear observers for autonomous Lipschitz continuous systems," IEEE Trans. Automat. Control, vol. 48, no. 3, pp. 451-464, Mar. 2003.
20. A. J. Krener and W. Respondek, "Nonlinear observers with linearizable error dynamics," SIAM J. Control Optim., vol. 23, no. 2, pp. 197-216, 1985.
21. W. Lin and C. I. Byrnes, "Remarks on linearization of discrete-time autonomous systems and nonlinear observer design," Syst. Control Lett., vol. 25, no. 1, pp. 31-40, 1995.
22. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, no. 6, pp. 789-814, 2000.
23. M. J. Messina, S. E. Tuna, and A. R. Teel, "Discrete-time certainty equivalence output feedback: Allowing discontinuous control laws including those from model predictive control," Automatica, vol. 41, no. 4, pp. 617-628, 2005.
24. H. Michalska and D. Q. Mayne, "Moving horizon observers and observer-based control," IEEE Trans. Automat. Control, vol. 40, no. 6, pp. 995-1006, Jun. 1995.
25. P. E. Moraal and J. W. Grizzle, "Observer design for nonlinear systems with discrete-time measurements," IEEE Trans. Automat. Control, vol. 40, no. 3, pp. 395-404, Mar. 1995.
26. H. Nijmeijer and A. J. van der Schaft, Nonlinear Dynamical Control Systems. New York: Springer-Verlag, 1990.
27. W. Perruquetti, T. Floquet, and E. Moulay, "Finite-time observers: application to secure communication," IEEE Trans. Automat. Control vol. 53, no. 1, pp. 356-360, Feb. 2008.
28. S. Pinchuk, "A counterexamle to the strong real Jacobian conjecture," Mathematische Zeitschrift, vol. 217, no. 1, pp. 1-4, 1994.
29. C. V. Rao, J. B. Rawlings, and D. Q. Mayne, "Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximation," IEEE Trans. Automat. Control, vol. 48, no. 2, pp. 246-258, Feb. 2003.
30. K. Rieger, K. Schlacher, and J. Holl, "On the observability of discrete-time dynamic systems - A geometric approach," Automatica vol. 44, no. 8, pp. 2057-2062, 2008.
31. Y. Shen and X. Xia, "Uniformly observable and globally lipschitzian nonlinear systems admit semi-global finite-time observers," in Proc. 17th IFAC World Congress, Seoul, Korea, 2008, pp. 9846-9851.
32. Y. Shen and X. Xia, "Semi-global finite-time observers for nonlinear systems," Automatica, vol. 44, no. 12, pp. 3152-3156, 2008.
33. E. D. Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems. New York: Springer-Verlag, 1998.
34. M. Zeitz, "The extended luenberger observer for nonlinear systems," Syst. Control Lett., vol. 9, no. 2, pp. 149-156, 1987.