A new fuzzy impulsive control of chaotic systems based on T-S fuzzy model

IEEE Transactions on Fuzzy Systems

Volumn 19, Issue 2, 2011, Pages 393-398

  Liu, Yang ^a   Zhao, Shouwei ^b   Lu, Jianquan ^c,d  

^a ZHEJIANG NORMAL UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY OF ENGINEERING SCIENCE   (China)

^c SOUTHEAST UNIVERSITY   (China)

^d POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

Author keywords

Chuas circuit; fuzzy impulsive control; Rsslers system; TakagiSugeno (T S) fuzzy model

Indexed keywords

CHUAS CIRCUIT; FUZZY IMPULSIVE CONTROL; IMPULSIVE CONTROL SYSTEMS; IMPULSIVE CONTROLS; IMPULSIVE INTERVALS; NUMERICAL SIMULATION; RSSLERS SYSTEM; STABILITY ISSUES; STABLE REGION; SUFFICIENT CONDITIONS; T-S FUZZY MODELS; TAKAGI-SUGENO MODELS; TAKAGISUGENO (T-S) FUZZY MODEL;

CONTROL SYSTEM STABILITY;

CHAOTIC SYSTEMS;

EID: 79953652678     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2010.2090162     Document Type: Article

References (32)

1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its application to modeling and control," IEEE Trans. Syst. Man, Cybern., vol. 15, no. SMC-15, pp. 116-132, Feb. 1985.
2. K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001.
3. K. Tanaka, T. Ikeda, and H. O. Wang, "A unified approach to controlling chaos via an LMI-based fuzzycontrol system design," IEEE Trans. Circ. Syst., vol. 45, no. 10, pp. 1021-1040, Oct. 1998. (Pubitemid 128745930)
4. C. W. Park, C. H. Lee, and M. Park, "Design of an adaptive model based controller for chaotic dynamics in Lorenz systems with uncertainty," Inf. Sci., vol. 147, pp. 245-266, 2002. (Pubitemid 35349793)
5. E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos," Phys. Rev. Lett., vol. 64, pp. 1196-1199, 1990.
6. Q. Gan and C. J. Harris, "Fuzzy local linearization and local basis function expansion in nonlinear system modeling," IEEE Trans. Syst. Man, Cybern., vol. 29, no. 4, pp. 559-565, Aug. 1999.
7. K. Y. Lian, C. S. Chiu, T-S. Chiang, and P. Liu, "LMI-based fuzzy chaotic synchronization and communications," IEEE Trans. Fuzzy Syst., vol. 9, no. 4, pp. 539-553, Aug. 2001. (Pubitemid 32933041)
8. Y. Wang, Z. H. Guan, and H. O. Wang, "Impulsive synchronization for Takagi-Sugeno fuzzy model and its application to continuous chaotic system," Phys. Lett. A, vol. 339, pp. 325-332, 2005. (Pubitemid 40591635)
9. Y. Wang, Z. H. Guan, H. O. Wang, and J. Xiao, "Impulsive control for T-S fuzzy system and its application to chaotic systems," Int. J. Bifurcat. Chaos, vol. 16, pp. 2417-2423, 2006. (Pubitemid 44671758)
10. J. Q. Lu, and J. D. Cao, "Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters," Chaos, vol. 15, no. 4, p. 043901-1-043901-10, 2005.
11. H. O. Wang, K. Tanaka, and M. Griffin, "An approach to fuzzy control of nonlinear systems: Stability and design issues," IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, Feb. 1996. (Pubitemid 126782417)
12. T. Yang, Impulsive Control Theory. Berlin/Heidelberg, Germany: Springer, 2001.
13. T. Yang, L. B. Yang, and C. M. Yang, "Impulsive control of Lorenz system," Physica D, vol. 110, pp. 18-24, 1997. (Pubitemid 127701586)
14. T. Yang and L. O. Chua, "Impulsive stabilization for control and synchronization of chaotic systems: Theory and application to secure communication," IEEE Trans. Circ. Syst., vol. 44, no. 10, pp. 976-988, Oct. 1997. (Pubitemid 127768200)
15. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations. Singapore: World Scientific, 1989.
16. Z. G. Li, C. Y. Wen, and Y. C. Soh, "Analysis and design of impulsive control systems," IEEE Trans. Automat. Control, vol. 46, no. 6, pp. 894-897, Jun. 2001. (Pubitemid 32609877)
17. M. Itoh, T. Yang, and L. O. Chua, "Conditions for impulsive synchronization of chaotic and hyperchaotic systems," Int. J. Bifurcat. Chaos, vol. 11, pp. 551-560, 2001.
18. Y. Liu and S. W. Zhao, "A new approach for the impulsive stabilization of Liu's system," Commun. Theor. Phys., vol. 5, pp. 994-998, 2010.
19. Y. Liu and S.W. Zhao, "A new approach to practical stability of impulsive functional differential equations in terms of two measures," J. Comput. Appl. Math., vol. 223, pp. 449-458, 2009.
20. J. T. Sun, Y. P. Zhang, and Q. D. Wu, "Less conservative conditions for asymptotic stability of impulsive control systems," IEEE Trans. Automat. Control, vol. 48, no. 5, pp. 829-831, May 2003.
21. S. W. Zhao and J. T. Sun, "A Lie algebraic condition of stability for hybrid systems and application to hybrid synchronization," Int. J. Bifurcat. Chaos, vol. 19, pp. 379-386, 2009.
22. Y. W. Wang, Z. H. Guan, and J. W. Xiao, "Impulsive control for synchronization of a class of continuous systems," Chaos, vol. 14, pp. 199-203, 2004.
23. X. Z. Liu, "Impulsive stabilization and control of chaotic system," Nonlinear Anal., vol. 47, pp. 1081-1092, 2001.
24. C. Li and X. Liao, "Complete and lag synchronization of hyerchaotic systems using small impulsive," Chaos, Sol. Fract., vol. 22, pp. 857-867, 2004.
25. Y. B. Nian, andY. A. Zheng, "Synchronization for Rössler chaotic systems using fuzzy impulsive controls," in Proc. IIHMSP, 2007, pp. 179-182.
26. Y. A. Zheng and G. R. Chen, "Fuzzy impulsive control of chaotic systems based on T-S fuzzy model," Chaos, Sol. Fract., vol. 39, pp. 2002-2011, 2009.
27. Q. S. Zhong, J. F. Bao, Y. B. Yu, and X. F. Liao, "Impulsive control for T-S fuzzy model-based chaotic systems," Math. Comp. Sim., vol. 79, pp. 409-415, 2008.
28. Q. S. Zhong, J. F. Bao, and Y. B. Yu, "Impulsive control for T-S fuzzy model based time-delay chaotic systems", in Proc. ICCCAS, 2008, pp. 987-990.
29. X. W. Liu and S. M Zhong, "T-S fuzzy model-based impulsive control of chaotic systems with exponential decay rate," Phys. Lett. A, vol. 370, pp. 260-264, 2007.
30. X. H. Zhang, D. Li, and G.Yang, "Impulsive control of T-S fuzzy systems," in Proc. FSKD, 2007, pp. 321-325.
31. X. H. Zhang, A. Khadra, D. Li, and D. Yang, "Impulsive stability of chaotic systems represented by T-S model," Chaos Sol. Fract., vol. 41, pp. 1863-1869, 2009.
32. J. Q. Lu, D.W. C. Ho, and J. D. Cao, "A unified synchronization criterion for impulsive dynamical networks," Automatica, vol. 46, pp. 1215-1221, 2010.