Robust nonlinear HOO synchronization of chaotic Lur'e systems

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 44, Issue 10, 1997, Pages 891-904

  Suykens, Johan A K ^a   Curran, Paul F ^a   Vandewalle, Joos ^a   Chua, Leon O ^a  

^a Katholieke Universiteit Leuven   (Belgium)

Author keywords

Chua's circuit; Lur'e systems; Matrix inequalities; Parametric uncertainty; Synchronization

Indexed keywords

CHAOS THEORY; ERROR ANALYSIS; FEEDBACK CONTROL; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); SYNCHRONIZATION;

CHAOTIC LUR'E SYSTEMS; CHUA'S CIRCUIT;

OPTIMAL CONTROL SYSTEMS;

EID: 0031258418     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.633878     Document Type: Article

References (34)

1. S. Boyd and C. Barratt, Linear Controller Design, Limits of Performance. Englewood Cliffs, NJ: Prentice-Hall, 1991.
2. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," SIAM (Studies in Applied Mathematics), vol. 15, 1994.
3. W.-K. Chen, Ed., The Circuits and Filters Handbook. Boca Raton, FL: CRC, 1995.
4. L. O. Chua, M. Komuro, and T. Matsumoto, "The double scroll family," IEEE Trans. Circuits Syst. I, vol. 33, pp. 1072-1118, Nov. 1986.
5. L. O. Chua, "Chua's circuit 10 years later," Int. J. Circuit Theory Applicat., vol. 22, pp. 279-305, 1994.
6. L. O. Chua and T. Roska, "The CNN paradigm," IEEE Trans. Circuits Syst. I, vol. 40, pp. 147-156, Mar. 1993.
7. P. F. Curran and L. O. Chua, "Absolute stability theory and the synchronization problem," Int. J. Bifurc. Chaos, 1997, to be published.
8. P. F. Curran, J. A. K. Suykens, and L. O. Chua, "Absolute stability theory and master-slave synchronization," Int. J. Bifurc. Chaos, 1997, to be published.
9. R. Fletcher, Practical Methods of Optimization. Chichester, U.K. and New York: Wiley, 1987.
10. C. Guzelis and L. O. Chua, "Stability analysis of generalized cellular neural networks," Int. J. Circuit Theory Applicat., vol. 21, pp. 1-33, 1993.
11. M. Hasler, "Synchronization principles and applications," in Circuits and Systems: Tutorials IEEE-ISCAS'94, pp. 314-326.
12. D. J. Hill and P. J. Moylan, "The stability of nonlinear dissipative systems," IEEE Trans. Automat. Contr., vol. AC-21, pp. 708-711, 1976.
13. Connections between finite-gain and asymptotic stability," IEEE Trans. Automat. Contr., vol. AC-25, pp. 931-936, Apr. 1980.
14. A. Isidori and A. Astolfi, "Disturbance attenuation and HO& control via measurement feedback in nonlinear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 1283-1293, 1992.
15. T. Kapitaniak and L. O. Chua, "Hyperchaotic attractors of unidirectionally-coupled Chua's circuits," Int. J. Bifurc. Chaos, vol. 4, no. 2, pp. 477-482, 1994.
16. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
17. P. E. Kloeden, E. Platen, and H. Schurz, "The numerical solution of nonlinear stochastic dynamical systems: A brief introduction," Int. J. Bifurc. Chaos, vol. 1, no. 2, pp. 277-286, 1991.
18. L. Kocarev, A. Shang, and L. O. Chua, "Transitions in dynamical regimes by driving: A unified method of control and synchronization of chaos," Int. J. Bifurc. Chaos, vol. 3, no. 2, pp. 479-483, 1993.
19. J. M. Maciejowski, Multivariable Feedback Design. Reading, MA: Addison-Wesley, 1989.
20. R. N. Madan, Guest Ed., Chua's Circuit: A Paradigm for Chaos. Signapore: World Scientific, 1993.
21. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems. New York: Springer-Verlag, 1989.
22. E. Polak and Y. Wardi, "Nondifferentiable optimization algorithm for designing control systems having singular value inequalities," Automatica, vol. 18, no. 3, pp. 267-283, 1982.
23. J. A. K. Suykens, J. P. L. Vandewalle, and B. L. R. De Moor, Artificial Neural Networks for Modeling and Control of Non-Linear Systems. Boston, MA: Kluwer Academic, 1996.
24. J. A. K. Suykens, P. F. Curran, and L. O. Chua, "Master-slave synchronization using dynamic output feedback," Int. J. Bifurc. Chaos, vol. 7, no. 3, pp. 671-679, 1997.
25. ∞ synchronization of chaotic Lur'e systems," Int. J. Bifurc. Chaos, vol. 7, no. 6, 1997, to be published.
26. J. A. K. Suykens, P. F. Curran, T. Yang, J. Vandewalle, and L. O. Chua, "Nonlinear HOC synchronization of Lur'e systems: Dynamic output feedback case," IEEE Trans. Circuits Syst. I, to be published.
27. J. A. K. Suykens, P. F. Curran, and L. O. Chua, "Robust synthesis for master-slave synchronization of Lur'e systems," submitted for publication.
28. J. A. K. Suykens, A. Huang, and L. O. Chua, "A family of n-scroll attractors from a generalized Chua's circuit," Int. J. Electron. Commun. Special Issue at the Occasion of Prof. Lueder's 65th Birthday, vol. 51, no. 3, pp. 131-138, 1997.
29. J. A. K. Suykens and L. O. Chua, "n-Double scroll hypercubes in ID-CNN's," Int. J. Bifurc. Chaos, vol. 7, no. 6, 1997.
30. A. van der Schaft, "L2-gain and passivity techniques in nonlinear control," Lecture Notes in Control and Information Sciences 218. New York: Springer-Verlag, 1996.
31. M. Vidyasagar, Nonlinear Systems Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1993.
32. J. C. Willems, "Dissipative dynamical systems I: General theory. II: Linear systems with quadratic supply rates," Archive Rational Mechan. Anal., vol. 45, pp. 321-343, 1972.
33. C. W. Wu and L. O. Chua, "A unified framework for synchronization and control of dynamical systems," Int. J. Bifurc. Chaos, vol. 4, no. 4, pp. 979-989, 1994.
34. C. W. Wu, T. Yang, and L. O. Chua, "On adaptive synchronization and control of nonlinear dynamical systems," Int. J. Bifurc. Chaos, vol. 6, no. 3, pp. 455-171, 1996.