Uniform invariance principle and synchronization. Robustness with respect to parameter variation

Journal of Differential Equations

Volumn 169, Issue 1, 2001, Pages 228-254

  Rodrigues, H M ^a   Alberto, L F C ^a   Bretas, N G ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Invariance principle; Synchronization

Indexed keywords

EID: 0035217310     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3902     Document Type: Article

References (25)

1. Afraimovich V. S., Rodrigues H. M. Uniform dissipativeness and synchronization on nonautonomous equations. Equadiff 95, International Conference on Differential Equations. 1998;World Scientific, Singapore. p. 3-17.
2. Affraimovich V. S., Verichev N. N., Rabinovich M. I. Stochastic synchronization of oscillation in dissipative systems. Izv. Vyssh. Uchebn. Zaved. Radiofiz. 29:1986;1050-1060.
3. Afraimovich V. S., Chow S.-N., Hale J. K. Synchronization in lattices of coupled oscillators. Physica D. 103:1997;442-451.
4. Carvalho A. N., Dłotko T., Rodrigues H. M. Upper semicontinuity of attractors and synchronization. J. Math. Anal. Appl. 220:1998;13-41.
5. H. D. Chiang, F. F. Wu, and, P. P. Varaya, A BCU method for direct analysis of power system transient stability, in, IEEE/PES, Summer Meeting, San Diego, CA, July 1991.
6. Chiang H. D., Wu F. F., Varaya P. P. Foundations of the potential energy boundary surface method for power system transient stability analysis. IEEE Trans. Circuits Systems. 35:1988.
7. Cuomo K. M., Oppenheim A. V. Chaotic signals and systems for communications. ICASSP. 1993.
8. Fujisaka H., Yamada T. Stability theory of synchronized motions in coupled oscillator systems. Prog. Theor. Phys. 69:1984;32-46.
9. Hale J. K., Lunel S. V. Introduction to Functional Differential Equations. Applied Mathematical Sciences. 99:1993;Springer-Verlag, Berlin/New York.
10. Hale J. K. Attracting manifolds for evolutionary equations. Resenhas IME-USP. 3:1997;55-72.
11. J. K. Hale, Diffusive Coupling, Dissipation and Synchronization, Technical Reports, CDSNS96-238.
12. Hale J. K. Dynamical systems and stability. J. Math. Anal. Appl. 26:1969;39-59.
13. LaSalle J. P. The extent of asymptotic stability. Proceedings of the National Academy of Sciences. March 1960;. p. 363-365.
14. LaSalle J. P. Some extensions of Liapunov's second method. IRE Trans. Circuit Theory. 7:1960;520-527.
15. LaSalle J. P. Asymptotic stability criteria. Proceedings of Symposia in Applied Mathematics. Hydrodynamic Instability. 13:1961;Amer. Math. Soc. Providence. p. 299-307.
16. LaSalle J. P. Stability theory for difference equations. Studies in ordinary differential equation. Stud. in Math. 14:1977;1-31.
17. Miller R. K. Asymptotic behavior of solutions of nonlinear differential equations. Trans. Amer. Math. Soc. 115:1965;400-416.
18. Pecora L. M., Carroll T. L., Johnson G. A., Mar D. J. Fundamentals of synchronization in chaotic systems, concepts and applications. Chaos. 7:1997;520-543.
19. Rodrigues H. M. Invariança para Sistemas não Autônomos de Equações Diferenciais com Retardamento e Aplicações. Escola de Engenharia de S. Carlos. 1970.
20. Rodrigues H. M. Abstract methods for synchronization and applications. Appl. Anal. 62:1996;263-296.
21. Rodrigues H. M., Alberto L. F. C., Bretas N. G. On the invariance principle. generalizations and applications to synchronization. IEEE Trans. Circuits Systems I. 47:2000;730-739.
22. Sell G. Nonautonomous differential equations and topological dynamics I, II. Trans. Amer. Math. Soc. 127:1967;241-262.
23. Slemrod M. Asymptotic behavior of a class of abstract dynamical systems. J. Differential Equations. 7:1970;584-600.
24. Wu C. W., Chua L. O. A unified framework for synchronization and control of dynamical systems. Int. J. Bifurcation Chaos. 4:1994;979-998.
25. Yang T., Chua L. O. Implusive stabilization for control and synchronization of chaotic systems: theory and application to secure communication. IEEE Trans. Circuits Systems. 44:1997;976-988.