Research PapersNo Access

DELAYED FEEDBACK SYNCHRONIZATION FOR TIME-DELAYED CHAOTIC SYSTEMS BASED ON T–S FUZZY MODEL

Division of Electronics & Control Engineering, Wonkwang University, 344-2 Shinyong-dong, Iksan 570-749, Korea

and

BK21 School for Creative Engineering Design of Next Generation Mechanical & Aerospace Systems, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Korea

Search for more papers by this author

https://doi.org/10.1142/S021798491002224XCited by:2 (Source: Crossref)

Abstract

In this letter, we propose a new synchronization method, called a delayed feedback fuzzy synchronization (DFFHS) method, for time-delayed chaotic systems with external disturbance. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the DFFHS controller is presented to not only guarantee aymptotical synchronization but also reduce the effect of external disturbance to an norm constraint. The proposed controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed DFFHS method.

Keywords:

References

L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1996). Crossref, Web of Science, ADS, Google Scholar
G. Chen and X. Dong , From Chaos to Order ( World Scientific , 1998 ) . Link, Google Scholar
C. C. Wang and J. P. Su, Chaos, Solitons & Fractals 20, 967 (2004). Crossref, Web of Science, ADS, Google Scholar
E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990). Crossref, Web of Science, ADS, Google Scholar
J. H. Park, Int. J. Nonlinear Sci. Numer. Simul. 6, 201 (2005). Web of Science, Google Scholar
X. S. Yang and G. Chen, Chaos, Solitons & Fractals 13, 1303 (2002). Crossref, Web of Science, ADS, Google Scholar
E. Bai and K. Lonngren, Phys. Rev. E 8, 51 (1997). Web of Science, Google Scholar
E. W. Bai and K. E. Lonngren, Chaos, Solitons & Fractals 11, 1041 (2000). Crossref, Web of Science, Google Scholar
O. M. Kwon and J. H. Park, Chaos, Solitons & Fractals 23, 445 (2005). Web of Science, Google Scholar
J. Hu, S. Chen and L. Chen, Phys. Lett. A 339, 455 (2005). Crossref, Web of Science, ADS, Google Scholar
M. Zhanet al., Phys. Rev. E 68, 6208 (2003). Google Scholar
K. Pyragas, Phys. Lett. A 170, 421 (1992). Crossref, Web of Science, ADS, Google Scholar
M. E. Yalcin, J. A. K. Suykens and J. Vandewalle, Int. J. Bifurcat. Chaos 11, 1707 (2001). Link, Web of Science, Google Scholar
X. X. Liao and G. R. Chen, Int. J. Bifurcat. Chaos 13, 207 (2003). Link, Web of Science, Google Scholar
F. L. Zhu, Phys. Lett. A 372, 223 (2008). Crossref, Web of Science, ADS, Google Scholar
T. Takagi and M. Sugeno, IEEE Trans. Syst. Man & Cybern. 15, 116 (1985). Web of Science, Google Scholar
K. Tanaka and M. Sugeno, Fuzzy Sets Syst. 45, 135 (1992). Crossref, Web of Science, Google Scholar
A. Stoorvogel , The ${\mathcal H}_\infty$ Control Problem: A State-Space Approach ( Prentice Hall, International , UK , 1992 ) . Google Scholar
Y. Y. Hou, T. L. Liao and J. J. Yan, Physica A 379, 81 (2007). Crossref, Web of Science, ADS, Google Scholar
C. K. Ahn, Phys. Lett. A 373, 1729 (2009). Crossref, Web of Science, ADS, Google Scholar
M. C. Mackey and L. Glass, Science 197, 287 (1977). Crossref, Web of Science, ADS, Google Scholar
J. D. Farmer, Physica D 4, 366 (1982). Crossref, Web of Science, Google Scholar
H. Lu, Phys. Lett. A 298, 109 (2002). Crossref, Web of Science, ADS, Google Scholar
Y. C. Tian and F. Gao, Physica D 117, 1 (1998). Crossref, Web of Science, ADS, Google Scholar
J. H. Park and O. M. Kwon, Chaos, Solitons & Fractals 27, 1011 (2006). Crossref, Web of Science, Google Scholar
B. Chen, X. Liu and S. Tong, Chaos, Solitons & Fractals 34, 1683 (2007). Crossref, Web of Science, ADS, Google Scholar
X. Guanet al., Physica D 227, 36 (2007). Crossref, Web of Science, ADS, Google Scholar
M. Chen and W. H. Chen, Chaos, Solitons & Fractals 41, 2716 (2009). Crossref, Web of Science, ADS, Google Scholar
W. Zhu, D. Xu and Y. Huang, Chaos, Solitons & Fractals 35, 904 (2008). Crossref, Web of Science, ADS, Google Scholar
X. Liu , Nonlinear Analysis: Theory, Methods & Applications ( 2009 ) , DOI: 10.1016/j.na.2009.01.162 . Google Scholar
S. Boyd et al. , Linear Matrix Inequalities in Systems and Control Theory ( SIAM , Philadelphia, PA , 1994 ) . Crossref, Google Scholar
E. Noldus, Int. J. Control 41, 947 (1985). Crossref, Web of Science, Google Scholar
P. Gahinet et al. , LMI Control Toolbox ( The Mathworks Inc. , 1995 ) . Google Scholar
L. Liet al., Chaos, Solitons & Fractals 41, 783 (2009). Crossref, Web of Science, ADS, Google Scholar