Bifurcation analysis of time-delay control systems with saturation

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 9, Issue 6, 1999, Pages 1089-1109

  Pagano, Daniel J ^a   Ponce, Enrique ^b   Aracil, Javier ^b  

^a FEDERAL UNIVERSITY OF SANTA CATARINA   (Brazil)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040122044     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127499000754     Document Type: Review

References (24)

1. Alvarez, J., Suárez, R. & Alvarez, J. [1993] "Planar linear systems with single saturated feedback," Syst. Control Lett. 20, 319-326.
2. Cook, P. A. [1994] Nonlinear Dynamical Systems (Prentice Hall).
3. Genesio, R. & Tesi, A. [1992] "Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems," Automatica 28(3), 531-548.
4. Gilli, M. & Maggio, G. M. [1996] "Predicting chaos through an harmonic balance technique: An application to the time-delayed Chua's circuit," IEEE Trans. Circuits Syst. I 43, 872-874.
5. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, NY).
6. Hale, J. & Koçak, H. [1991] Dynamics and Bifurcations (Springer-Verlag).
7. Khalil, H. [1996] Nonlinear Systems, 2nd edition (Prentice Hall, Upper Saddle River, NJ).
8. Kolmanovskii, V. & Myshkis, A. [1992] Applied Theory of Functional Differential Equations, Mathematics and its Applications, Soviet Series (Kluwer Academis Publishers), pp. 117-118.
9. Kuznetzov, Y. A. [1995] Elements of Applied Bifurcation Theory, Applied Mathematical Sciences 112 (Springer-Verlag).
10. Llibre, L. & Sotomayor, J. [1996] "Phase portraits of planar control systems," Nonlin. Anal. Theor. Methods Appl. 27(10), 1177-1197.
11. Llibre, J. & Ponce, E. [1996] "Global first harmonic bifurcation diagram for odd piecewise linear control systems," Dyn. Stab. Syst. 11(1), 49-88.
12. Llibre, J. & Ponce, E. [1998] "Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields," Nonlin. Anal. TMA 36(5), 623-653.
13. Luzyanina, T., Engelborghs, K., Lust, K. & Roose, D. [1997] "Computation, continuation and bifurcation analysis of periodic solutions of delay differential equations," Int. J. Bifurcation and Chaos 7(11), 2547-2560.
14. Mees, A. I. & Chua, L. O. [1979] "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circuits Syst. 26, 235-254.
15. Moiola, J. & Chen, G. [1993] "Frequency domain approach to computation and analysis of bifurcations and limit cycles: A tutorial," Int. J. Bifurcation and Chaos 4(3), 843-867.
16. Moiola, J., Chiachiarini, H. & Desages, A. C. [1996] "Bifurcation and Hopf degeneracies in nonlinear feedback systems with time-delay," Int. J. Bifurcation and Chaos 6(4), 661-672.
17. Nayfeh, A. & Balachandran, B. [1992] Applied Nonlinear Dynamics (John Wiley).
18. Pagano, D. J., Ponce, E. & Aracil, J. [1997] "Bifurcation analysis of low-order nonlinear control systems with delay," Proc. Control of Oscillations and Chaos (COC97) 3, eds. Chernousko, F. L. & Fradkov, A. L., St. Petesburg, Russia, pp. 478-483.
19. Ponce, E., Alamo, T. & Aracil, J. [1996] "Robustness and bifurcations for a class of piecewise linear control systems," Proc. 13th World Congress of IFAC, San Francisco, USA, E, pp. 61-66.
20. Strogatz, S. [1995] Nonlinear Dynamics and Chaos (Addison-Wesley).
21. Tesi, A., Abed, E. H., Genesio, R. & Wang, H. O. [1996] "Harmonic balance analysis of period-doubling bifurcations with implications for control of nonlinear dynamics," Automatica 32(9), 1255-1271.
22. Tsypkin, Ya. Z. [1946] "Stability of systems with delayed feedback," Avtomat. Telemekh. 7, 107-129; also in MacFarlane, A. G. (ed.) [1979], Frequency Response Methods in Control Systems (IEEE Press), pp. 45-56.
23. Tsypkin, Ya. Z. [1946] "Stability of systems with delayed feedback," Avtomat. Telemekh. 7, 107-129; also in MacFarlane, A. G. (ed.) [1979], Frequency Response Methods in Control Systems (IEEE Press), pp. 45-56.
24. Wang, H. & Abed, E. [1995] "Bifurcation control of a chaotic system," Automatica 31(9), 1213-1226.