Sliding mode observers and observability singularity in chaotic synchronization

Mathematical Problems in Engineering

Volumn 2004, Issue 1, 2004, Pages 11-31

  Boutat Baddas, L ^a   Barbot, J P ^a   Boutat, D ^b   Tauleigne, R ^c  

^a Equips Commande des Systemes ENSEA   (France)

^b UNIVERSITÉ D'ORLÉANS   (France)

^c Bioinformatique et Chimie Moléculaire   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DATA COMMUNICATION SYSTEMS; INFORMATION DISSEMINATION; LOGIC DESIGN; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; SYNCHRONIZATION;

ADAPTIVE CONTROLLER; CHAOTIC SYSTEMS; INFORMATION TRANSFER; LOWPASS FILTERS;

CHAOS THEORY;

EID: 4744357453     PISSN: 1024123X     EISSN: None     Source Type: Journal    
DOI: 10.1155/S1024123X04309038     Document Type: Article

References (24)

1. J. P. Barbot, I. Belmouhoub, and L. Boutat-Baddas, Observability normal forms, New Trends in Nonlinear Dynamics and Control, and Their Applications (W. Kang, M. Xiao, and C. Borges, eds.), Lecture Notes in Control and Inform. Sci., vol. 295, Springer, Berlin, 2003, pp. 3-17.
2. J. P. Barbot, T. Boukhobza, and M. Djemai, Sliding mode observer for triangular input form, Proc. 35th IEEE Conference on Decision and Control, Kobe, 1996, pp. 1489-1490.
3. G. Besançon, A viewpoint on observability and observer design for nonlinear systems, New Directions in Nonlinear Observer Design (Geiranger Fjord, 1999) (H. Nimeijer and T. I. Fossen, eds.), Lecture Notes in Control and Inform. Sci., vol. 244, Springer-Verlag, London, 1999, pp. 3-22.
4. L. Boutat-Baddas, D. Boutat, J. P. Barbot, and R. Tauleigne, Quadratic observability normal form, Proc. 40th IEEE Conference on Decision and Control, Florida, 2001, pp. 2942-2947.
5. P. Brunovský, A classification of linear controllable systems, Kybernetika (Prague) 6 (1970), 173-188.
6. G. Chen and X. Dong, From Chaos to Order. Methodologies, Perspectives and Applications, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises, vol. 24, World Scientific Publishing, New Jersey, 1998.
7. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, Synchronization of Lorenz-based chaotic circuit with application to communications, IEEE Trans. Circuits and Systems 40 (1993), 626-633.
8. J.-P. Gauthier and G. Bornard, Observability for any u(t) of a class of nonlinear systems, IEEE Trans. Automat. Control 26 (1981), no. 4, 922-926.
9. P. Glendinning, Stability, Instability and Chaos: an Introduction to the Theory of Nonlinear Differential Equations, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1994.
10. R. Hermann and A. J. Krener, Nonlinear controllability and observability, IEEE Trans. Automat. Control 22 (1977), no. 5, 728-740.
11. W. Kang and A. J. Krener, Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems, SIAM J. Control Optim. 30 (1992), no. 6, 1319-1337.
12. P. V. Kokotović, R. E. O'Malley Jr., and P. Sannuti, Singular perturbations and order reduction in control theory - an overview, Automatica J. IFAC 12 (1976), no. 2, 123-132.
13. A. J. Krener and A. Isidori, Linearization by output injection and nonlinear observers, Systems Control Lett. 3 (1983), no. 1, 47-52.
14. A. J. Krener and M. Q. Xiao, Nonlinear observer design in the Siegel domain, SIAM J. Control Optim. 41 (2002), no. 3, 932-953.
15. H. Nijmeijer and I. M. Y. Mareels, An observer looks at synchronization, IEEE Trans. Circuits Systems I Fund. Theory Appl. 44 (1997), no. 10, 882-890.
16. U. Parlitz, L. O. Chua, L. j. Kocarev, K. S. Halle, and A. Shang, Transmission of digital signals by chaotic synchronization, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 2 (1992), no. 4, 973-997.
17. W. Perruquetti and J. P. Barbot, Sliding Mode Control in Engineering, Marcel Dekker, Oregon, 2002.
18. F. Plestan and A. Glumineau, Linearization by generalized input-output injection, Systems Control Lett. 31 (1997), no. 2, 115-128.
19. H. Sira-Ramirez and C. Cruz-Hernandez, Synchronization of chaotic systems: a generalized Hamiltonian systems approach, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 11 (2001), no. 5, 1381-1395.
20. A. N. Tikhonov, Systems of differential equations containing small parameters multiplying the derivative, Mat. Sb. (N.S.) 31 (1952), 575-586 (Russian).
21. V. I. Utkin, Sliding Modes in Control and Optimization, Communications and Control Engineering Series, Springer-Verlag, Berlin, 1992.
22. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Texts in Applied Mathematics, vol. 2, Springer-Verlag, New York, 1990.
23. Y. Xiong and M. Saif, Sliding mode observer for nonlinear uncertain systems, IEEE Trans. Automat. Control 46 (2001), no. 12, 2012-2017.
24. T. Yang and L. Chua, Secure communication via chaotic parameter modulation, IEEE Trans. Circuits Systems I Fund. Theory Appl. 43 (1996), no. 9, 817-819.