Finite-time observers: Application to secure communication

IEEE Transactions on Automatic Control

Volumn 53, Issue 1, 2008, Pages 356-360

  Perruquetti, Wilfrid ^a,b   Floquet, Thierry ^a,b   Moulay, Emmanuel ^c  

^a ECOLE CENTRALE DE LILLE   (France)

^b L'Institut National de Recherche en Informatique et en Automatique (INRIA)   (France)

^c CNRS   (France)

Author keywords

Finite time synchronization; Secure communication; Two channel transmission

Indexed keywords

CANONICAL FORM; CHAOS SYNCHRONIZATION; FINITE-TIME CONVERGENCE; HOMOGENEITY PROPERTIES; OBSERVER DESIGN; OUTPUT INJECTION; SECURE COMMUNICATIONS; SECURE DATA; TIME SYNCHRONIZATION; TWO-CHANNEL;

NONLINEAR SYSTEMS; SYNCHRONIZATION;

CHAOS THEORY;

EID: 56349118144     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.914264     Document Type: Article

References (38)

1. L. M. Pecora and T. L. Carroll, "Synchronization in chaotic systems," Phys. Rev. Lett., vol. 64, pp. 821-824, 1990.
2. H. Nijmeijer and I. M. Y. Mareels, "An observer looks at synchronization," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl, vol. 44, no. 10, pp. 882-890, Oct. 1997.
3. A. Fradkov, H. Nijmeijer, and A. Markov, "Adaptive observer-based synchronization for communication," Int. J. Bifur. Chaos Appl Sci. Eng., vol. 10, no. 12, pp. 2807-2813, 2000.
4. S. Mascolo and G. Grassi, "Controlling chaos via backstepping design," Phys. Rev. E (3), vol. 56, no. 5, pp. 6166-6169, 1997.
5. D. López-Mancilla, C. Cruz-Hernández, and C. Posadas-Castillo, "A modified chaos-based communication scheme using Hamiltonian forms and observer," J. Phys.: Conf. Ser., vol. 23, pp. 267-275, 2005.
6. G. Grassi and S. Mascolo, "Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl, vol. 44, no. 10, pp. 1011-1014, Oct. 1997.
7. 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.
8. F. Sauvage, M. Guay, and D. Dochain, "Design of a nonlinear finite-time converging observer for a class of nonlinear systems," J. Control Sci. Eng., vol. 2007, pp. 36954-1-36954-9, 2007.
9. S. V. Drakunov and V. I. Utkin, "Sliding mode observers tutorial," in Proc. 34th IEEE Conf. Decis. Control, 1995, pp. 3376-3378.
10. W. Perruquetti, T. Floquet, and P. Borne, "A note on sliding observer and controller for generalized canonical forms," in Proc. IEEE Conf. Decis. Control, Tampa, FL, 1998, pp. 1920-1925.
11. M. Fliess and H. Sira-Ram'rez, "Reconstructeurs d'état," C. R. Acad. Sci. Paris Ser. I Math, vol. 338, pp. 91-96, 2004.
12. H. Sira-Ram'rez and M. Fliess, "An algebraic state estimation approach for the recovery of chaotically encrypted messages," Int. J. Bifur. Chaos Appl. Sci. Eng., vol. 16, pp. 295-309, 2006.
13. Z. P. Jiang, "A note on chaotic secure communication systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 49, no. 1, pp. 92-96, Jan. 2002.
14. T. Yang and L. Chua, "Secure communication via chaotic parameter modulation," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43, no. 9, pp. 817-819, Sep. 1996.
15. R. Lozi, "Secure communications via chaotic synchronization in Chua's circuit and Bonhoeffer-van der Pol equation: Numerical analysis of the errors of the recovered signal," in Proc. IEEE Int. Symp. Circuits Syst., Seattle, WA, 1995, pp. 684-687.
16. M. Itoh, H. Murakami, and L. Chua, "Performance of Yamakawa's chaotic chips and Chua's circuits for secure communications," in Proc. IEEE Int. Symp. Circuits Syst., London, U.K., 1994, vol. 6, pp. 105-108.
17. R. Hermann and A. J. Krener, "Nonlinear controllability and observability," IEEE Trans. Autom. Control, vol. AC-22, no. 5, pp. 728-740, Oct. 1977.
18. A. Glumineau, C. H. Moog, and F. Plestan, "Algebra-geometric conditions for the linearization by input-output injection," IEEE Trans. Autom, Control, vol. 41, no. 4, pp. 598-603, Apr. 1996.
19. A. J. Krener and A. Isidori, "Linearization by output injection and nonlinear observers," Syst. Control Lett., vol. 3, pp. 47-52, 1983.
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. X. H. Xia and W. B. Gao, "Nonlinear observer design by observer error linearization," SIAM J. Control Optim., vol. 27, pp. 199-216, 1989.
22. J. Back, K. T. Yu, and J. H. Seo, "Dynamic observer error linearization," Autom. J. IFAC, vol. 42, pp. 2195-2200, 2006.
23. P. Jouan, "Immersion of nonlinear systems into linear systems modulo output injection," SIAM J. Control Optim., vol. 41, no. 6, pp. 1756-1778, 2003.
24. 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.
25. A. Bacciotti and L. Rosier, Liapunov Functions and Stability in Control Theory, 2nd ed. Berlin, Germany: Springer-Verlag, 2005.
26. E. Moulay and W. Perruquetti, "Finite time stability of non linear systems," in Proc. IEEE Conf. Decis. Control, Lahaina, HI, Dec. 2003, vol. 4, pp. 3641-3646.
27. W. Perruquetti and S. Drakunov, "Finite time stability and stabilisation," in Proc. IEEE Conf. Decis. Control, Sydney, Australia, 2000, vol. 2, pp. 1894-1899.
28. E. Moulay and W Perruquetti, "Finite time stability of differential inclusions," IMA J. Math. Control Inf., vol. 22, pp. 465-475, 2005.
29. S. P. Bhat and D. S. Bernstein, "Geometric homogeneity with applications to finite-time stability," Math. Control. Signal Syst., vol. 17, pp. 101-127, 2005.
30. V. T. Haimo, "Finite time controllers," SIAM J. Control Optim., vol. 24, no. 4, pp. 760-770, 1986.
31. Y. Hong, J. Huang, and Y. Xu, "On an output feedback finite-time stabilization problem," IEEE Trans. Autom. Control, vol. 46, no. 2, pp. 305-309, Feb. 2001.
32. E. Moulay and W. Perruquetti, "Finite-time stability and stabilization: State of the art," in in Advances in Variable Structure and Sliding Mode Control (Lecture Notes in Control and Information Sciences), vol. 334. New York: Springer-Verlag, 2006.
33. 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.
34. Y. Orlov, "Finite time stability of homogeneous switched systems," in Proc. IEEE Conf. Decis. Control, Lahaina, HI, Dec. 2003, vol. 4, pp. 4271-4276.
35. L. Rosier, "Homogeneous Lyapunov function for homogeneous continuous vector field," Syst. Control Lett., vol. 19, pp. 467-473, 1992.
36. M. Y. Chen, Z. Z. Han, and Y. Shang, "General synchronization of Genesio-Tesi systems," Int. J. Bifur. Chaos Appl. Sei. Eng., vol. 14, pp. 347-354, 2004.
37. M. Feki, "Observer-based exact synchronization of ideal and mismatched chaotic systems," Phys. Lett. A, vol. 309, pp. 53-60, 2003.
38. J. Barbot, I. Belmouhoub, and L. Boutat-Baddas, "Observability normal forms," in in New Trends in Nonlinear Dynamics and Control and Their Applications (Lecture Notes in Computer Science), vol. 295. New York: Springer-Verlag, 2004.