Delay-dependent approach to stabilization of time-delay chaotic systems via standard and delayed feedback controllers

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 15, Issue 4, 2005, Pages 1455-1465

  Xu, Shengyuan ^a   Lam, James ^b   Zou, Yun ^a  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Chaos control; Chaotic systems; Time delay systems; Time delayed feedback

Indexed keywords

CONTROL EQUIPMENT; DELAY CIRCUITS; FEEDBACK CONTROL; MATRIX ALGEBRA; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; STABILIZATION; THEOREM PROVING;

CHAOS CONTROL; CHAOTIC SYSTEMS; TIME-DELAY SYSTEMS; TIME-DELAYED FEEDBACK;

CHAOS THEORY;

EID: 22144498867     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405012570     Document Type: Article

References (26)

1. Bollt, E. M. [2003] "Review of chaos communication by feedback control of symbolic dynamics," Int. J. Bifurcation and Chaos 13, 269-285.
2. Boyd, S., El Ghaoui, L., Feron, E. & Balakrishnan, V. [1994] Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics (SIAM, Philadelphia, PA).
3. Chen, G. & Dong, X. [1998] From Chaos to Order: Methodologies, Perspectives and Applications (World Scientific, Singapore).
4. Chen, G. & Lai, D. [1998] "Feedback anticontrol of 'discrete chaos," Int. J. Bifurcation and Chaos 8, 1585-1590.
5. Chen, G. [2001] "What does chaos have to do with systems and control engineering?" J. Syst. Sci. Compl. 14, 31-39.
6. El Ghaoui, L., Oustry, F. & Aitrami, M. [1997] "A cone complementarity linearization algorithm for static output-feedback and related problems," IEEE Trans. Automat. Contr. 42, 1171-1176.
7. Feki, M. [2003] "An adaptive chaos synchronization scheme applied to secure communication," Chaos Solit. Fract. 18, 141-148.
8. Guan, X., Chen, C., Peng, H. & Fan, Z. [2003] "Time-delayed feedback control of time-delay chaotic systems," Int. J. Bifurcation and Chaos 13, 193-205.
9. Hale, J. K. [1977] Theory of Functional Differential Equations (Springer-Verlag, NY).
10. Kolmanovskii, V. B. & Myshkis, A. D. [1999] Introduction to the Theory and Applications of Functional Differential Equations (Kluwer Academic Publishers, Dordrecht).
11. Lenci, S. & Rega, G. [2003] "Optimal numerical control of single-well to cross-well chaos transition in mechanical systems," Chaos Solit. Fract. 15, 173-186.
12. Li, X. & de Souza, C. E. [1997] "Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach," IEEE Trans. Automat. Contr. 42, 1144-1148.
13. Lu, H., He, Y. & He, Z. [1998] "A chaos-generator: 'Analyses of complex dynamics of a cell equation in delayed cellular neural networks," IEEE Trans. Circuits Syst.-I 45, 178-181.
14. Mackey, M. C. & Glass, L. [1977] "Oscillation and chaos in physiological control systems," Science 197, 287-289.
15. Ott, E., Grebogi, C. & Yorke, J. A. [1990] "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199.
16. Pyragas, K. [1992] "Continuous control of chaos by self-controlling feedback," Phys. Lett. A170, 421-428.
17. Shobukhov, A. [1998] "Complex dynamic behavior in a model of electro-optic device with time-delayed feedback," Int. J. Bifurcation and Chaos 8, 1347-1354.
18. Sun, J. [2004] "Delay-dependent stability criteria for time-delay chaotic systems via time-delay feedback control," Chaos Solit. Fract. 21, 143-150.
19. Tian, Y.-C. & Gao, F. [1998] "Adaptive control of continuous-time systems with delay," Physica D117, 1-12.
20. Ushio, T. [1996] "Limitation of delayed feedback control in nonlinear discrete-time systems," IEEE Trans. Circuits Syst.-I 43, 815-816.
21. Wang, X. & Chen, G. [1999] "On feedback anticontrol of discrete chaos," Int. J. Bifurcation and Chaos 9, 1435-1441.
22. Wang, X., Chen, G. & Yu, X. [2000] "Anticontrol of chaos in continuous-time systems via time-delay feedback," Chaos 10, 771-779.
23. ∞ and positive real control for linear neutral delay systems," IEEE Trans. Automat. Contr. 46, 1321-1326.
24. Xu, S., Lam, J. & Yang, C. [2001b] "Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay," Syst. Contr. Lett 43, 77-84.
25. Xu, S., Lam, J. & Yang, C. [2002] "Robust stability analysis and stabilization for uncertain linear neutral delay systems," Int. J. Syst. Sci. 33, 1195-1206.
26. Yamapi, R., Chabi Orou, J. B. & Woafo, P. [1999] "Harmonic oscillations, stability and chaos control in a non-linear electromechanical system," J. Sound Vibr. 259, 1253-1264.