Observability quadratic normal form for discrete-time systems

IEEE Transactions on Automatic Control

Volumn 50, Issue 7, 2005, Pages 1031-1038

  Belmouhoub, Inam ^a   Djemai M ^a   Barbot, J P ^a  

^a ENSEA   (France)

Author keywords

Chaotic systems synchronization; Observability normal form; Quadratic equivalence; Reduced observer design

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; COMPUTER SIMULATION; CONTROL THEORY; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; OBSERVABILITY; POLYNOMIALS; THEOREM PROVING; VECTORS;

CHAOTIC SYSTEMS SYNCHRONIZATION; OBSERVABILITY NORMAL FORM; QUADRATIC EQUIVALENCE; REDUCED OBSERVER DESIGN;

DISCRETE TIME CONTROL SYSTEMS;

EID: 23144458350     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2005.851450     Document Type: Article

References (25)

1. K. J. Astorm and B. Wittermark, Computer Controlled Systems, Theory and Design. Upper Saddle River, NJ: Prentice-Hall, 1990.
2. J.-P. Barbot, S. Monaco, and D. Normand-Cyrot, "Quadratic forms and approximate feedback linearization in discrete time," Int. J. Control, vol. 67, no. 4, pp. 567-586, 1997.
3. D. Boutat and J.-P. Barbot, "Poincaré normal form for a class of driftless system in one-dimensional submanifold neighborhood," Math. Control, Signals, Syst., vol. 15, pp. 256-274, 2002.
4. L. Boutat-Baddas, D. Boutat, J.-P. Barbot, and R. Tauleigne, "Quadratic observability normal form," in Proc. 40th IEEE Conf. Decision Control, Orlando, FL, Dec. 2001, pp. 2942-2497.
5. C. Canudas De Wit, A. Youssef, J. P. Barbot, P. Martin, and F. Malrait, "Observability conditions of induction motors at low frequencies" Proc. 139th EEE Conf. Decision Control, pp. 2044-2049, Dec. 2000.
6. F. Gordillo, F. Salas, R. Ortega, and J. Aracil, "Hopf bifurcation in indirect field-oriented control of induction motors," Automatica, vol. 38, no. 5, pp. 829-835, 2002.
7. G. Gu, A. Sparks, and W. Kang, "Bifurcation analysis and control for surge model via the projection method," in Proc. Amer. Control Conf., 1998, pp. 3617-3621.
8. B. Hamzi, J.-P. Barbot, S. Monaco, and D. Normand-Cyrot, "Nonlinear discrete-time control of systems with a Naimar-Sacker bifurcation," Syst. Control Lett., vol. 44, pp. 245-258, 2001.
9. H. J. C. Huijberts, T. Lilge, and H. Nijmeijer, "Nonlinear discrete-time synchronization via extended observers," Int. J. Bifurcation Chaos, vol. 11, no. 7, pp. 1997-2006, 2001.
10. W. Kang, "Bifurcation and normal form of nonlinear control system: Part I and II," SIAM J. Control Optim., vol. 36, pp. 193-232, 1998.
11. W. Kang and A. J. Krener, "Extended quadratic controller normal form and dynamic state feedback linearization of non linear systems," SIAM J. Control Optim., vol. 30, no. 6, pp. 1319-1337, 1992.
12. A. J. Krener, Feedback Linearization Mathematical Control Theory, J. Bailleul and J.-C. Willems, Eds. New York: Springer-Verlag, 1998, pp. 66-98. Math. Control Theory.
13. A. J. Krener, "Approximate linearization by state feedback and coordinate change," Syst. Control Lett., vol. 5, pp. 181-185, 1983.
14. A. J. Krener and L. Li, "Normal forms and bifurcations of discrete time nonlinear control systems," SIAM J. Control Optim., vol. 40, pp. 1697-1723, 2002.
15. A. J. Krener and M. Xiao, "Nonlinear observer design in the siegel domain," SIAM J. Control Optim., vol. 41, no. 3, pp. 932-953, 2002.
16. A. J. Krener and M. Xiao, "Observers for linearly unobservable nonlinear systems," Syst. Control Lett., vol. 46, pp. 281-288, 2002.
17. T. Lilge, "Nonlinear discrete-time observers for synchronization problems," LNCIS 244, New Direction in Nonlinear Observer Design, pp. 491-510, 1999.
18. W. Lin and C. I. Byrnes, "Remarks on linearization of discrete-time autonomous systems and linear observation design," Syst. Control Lett., vol. 25, pp. 31-40, 1995.
19. W. Lin and C. I. Byrnes, Zero-State Observability and Stability of Discrete-Time Nonlinear Systems. Washington, DC: ACC, 1995.
20. H. Nijmeijer and I. M. Y. Mareels, "An observer looks at synchronization," IEEE Trans. Circuits Syst. I, Fundamental Theory Appl., vol. 44, no. 11, pp. 882-891, 1997.
21. U. Parlitz, L. O. Chua, L. Kocarev, K. S. Halle, and A. Shang, "Transmission of digital signals by chaotic synchronization," Int. J. Bifurcation Chaos, vol. 2, no. 4, pp. 973-997, 1992.
22. H. Poincaré, "Les Méthodes nouvelles de la mécanique céleste" (in French), Gauthier Villard, 1987.
23. A. Rapaport and A. Maloum, "Embedding for exponential observers of nonlinear systems," presented at the 39th IEEE Conf. Decision Control, Sidney, NSW, Australia, 2000.
24. C. Aguilar, M. Castañón, and H. Sira-Ramírez, "Exact state reconstructors in the recovery of messages encrypted by the states of nonlinear discrete-time chaotic systems," Int. J. Bifurcation Chaos, vol. 12, no. 1, pp. 169-177, 2002.
25. I. A. Tall and W. Respondek, "Normal forms and invariants of nonlinear single-input systems with noncontrollable linearization," in Proc. IFAC IFA-NOLCOS, 2001, pp. 122-127.