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MASTER-SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS BASED ON TIME-VARYING DELAY FEEDBACK CONTROL

HE HUANG

Department of Computer Science and Engineering, Southeast University, Nanjing 210096, P. R. China

Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, P. R. China

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and

JINDE CAO

Department of Mathematics, Southeast University, Nanjing 210096, P. R. China

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https://doi.org/10.1142/S021812740701969XCited by:15 (Source: Crossref)

Abstract

This paper deals with the master-slave synchronization problem of Lur'e systems based on time-varying delay feedback control. The time-varying delay is only assumed to be bounded. Delay-dependent conditions are derived such that the controlled slave system can track the master system. The synchronization criteria are expressed in terms of linear matrix inequality, which can be checked readily by using some standard numerical packages. A simulation example is provided to demonstrate the effectiveness of the proposed approach.

Keywords:

References

S. Boyd et al. , Linear Matrix Inequalities in System and Control Theory ( SIAM , Philadelphia, PA , 1994 ) . Crossref, Google Scholar
R. Brown and L. Kocarev, Chaos 10, 344 (2000), DOI: 10.1063/1.166500. Crossref, Web of Science, Google Scholar
J. Cao, H. X. Li and D. W. C. Ho, Chaos Solit. Fract. 23, 1285 (2005). Crossref, Web of Science, Google Scholar
G. Chen and X. Dong , From Chaos to Order-Perspectives, Methodologies, and Applications ( World Scientific , Singapore , 1998 ) . Crossref, Google Scholar
H. F. Chen and J. M. Liu, IEEE J. Quant. Electron. 36, 27 (2000), DOI: 10.1109/3.817635. Crossref, Web of Science, Google Scholar
C. J. Chenget al., IEEE Trans. Syst. Man Cybern.-B 36, 209 (2006), DOI: 10.1109/TSMCB.2005.856144. Crossref, Web of Science, Google Scholar
L. O. Chua, M. Komuro and T. Matsumoto, IEEE Trans. Circuits Syst.-I 33, 1072 (1986). Crossref, Web of Science, Google Scholar
P. F. Curran and L. O. Chua, Int. J. Bifurcation and Chaos 7, 1375 (1997). Link, Web of Science, Google Scholar
P. F. Curran, J. A. K. Suykens and L. O. Chua, Int. J. Bifurcation and Chaos 7, 2891 (1997). Link, Web of Science, Google Scholar
P. Gahinet et al. , LMI Control Toolbox: For Use With Matlab ( The Math Works, Inc. , 1995 ) . Google Scholar
K. Gu , V. Kharitonov and J. Chen , Stability of Time-Delay Systems ( Birkhauser , Boston , 2003 ) . Crossref, Google Scholar
K. Gu and S. I. Niculescu, ASME J. Dyn. Syst. Meas. Cont. 125, 158 (2003), DOI: 10.1115/1.1569950. Crossref, Web of Science, Google Scholar
H. Hasler, Synchronization principles and applications, Circuits and Systems: Tutorials IEEE-ISCAS'94 (1994) pp. 314–326. Google Scholar
M. Hasler, Y. Maistrenko and O. Popovich, Phys. Rev. E 58, 6843 (1998), DOI: 10.1103/PhysRevE.58.6843. Crossref, Web of Science, Google Scholar
H. Huang, H. X. Li and J. Zhong, Int. J. Bifurcation and Chaos 16, 281 (2006). Link, Web of Science, Google Scholar
V. B. Kolmanovskii and V. R. Nosov , Stability of Functional Differential Equations , Mathematics in Science and Engineering 180 ( Academic Press , NY , 1986 ) . Google Scholar
X. Liao and G. Chen, Int. J. Bifurcation and Chaos 13, 207 (2003). Link, Web of Science, Google Scholar
R. N. Madan (ed.) , Chua's Circuit: A Paradigm for Chaos ( World Scientific , Singapore , 1993 ) . Link, Google Scholar
S. I. Niculescuet al., IEEE Trans. Automat. Contr 43, 743 (1998), DOI: 10.1109/9.668851. Crossref, Web of Science, Google Scholar
L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1991), DOI: 10.1103/PhysRevLett.64.821. Crossref, Web of Science, Google Scholar
J. A. K. Suykenset al., IEEE Trans. Circuits Syst.-I 44, 891 (1997), DOI: 10.1109/81.633878. Crossref, Web of Science, Google Scholar
J. A. K. Suykens, J. Vandewalle and L. O. Chua, Int. J. Bifurcation and Chaos 7, 1323 (1997). Link, Web of Science, Google Scholar
J. A. K. Suykenset al., IEEE Trans. Circuits Syst.-I 44, 1089 (1997), DOI: 10.1109/81.641776. Crossref, Web of Science, Google Scholar
J. A. K. Suykens and J. Vandewalle, Int. J. Bifurcation and Chaos 7, 665 (1997). Link, Web of Science, Google Scholar
J. A. K. Suykens, P. F. Curran and L. O. Chua, IEEE Trans. Circuits Syst.-I 46, 841 (1999), DOI: 10.1109/81.774230. Crossref, Web of Science, Google Scholar
M. Vidyasagar , Nonlinear Systems Analysis ( Prentice-Hall , Englewood Cliffs, NJ , 1993 ) . Google Scholar
C. W. Wu and L. O. Chua, Int. J. Bifurcation and Chaos 4, 979 (1994). Link, Web of Science, Google Scholar
M. E. Yalçin, J. A. K. Suykens and J. Vandewalle, Int. J. Bifurcation and Chaos 11, 1707 (2001). Link, Web of Science, Google Scholar