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ESTIMATION OF AN ATTRACTION REGION IN ONE-DIMENSIONAL DELAYED-FEEDBACK CONTROL SYSTEMS

KEIJI KONISHI

Department of Complex Systems, Future University — Hakodate, 116–2 Kamedanakano, Hakodate, Hokkaido 041-8655, Japan

https://doi.org/10.1142/S0218127405012296Cited by:0 (Source: Crossref)

Abstract

This paper presents a simple numerical scheme for estimating the attraction region of a fixed point in one-dimensional discrete-time chaotic systems controlled by the delayed-feedback method. This scheme employs the well-known linear matrix inequality approach. A systematic procedure for estimating the region is provided, and numerical examples are used to validate the results.

Keywords:

References

P. V. Bayly and L. N. Virgin, Phys. Rev. E50, 604 (1994). Google Scholar
S. Bielawski, D. Derozier and P. Glorieux, Phys. Rev. A47, 2492 (1993). Google Scholar
S. Boyd et al. , Linear Matrix Inequalities in System and Control Theory ( SIAM , Philadelphia, PA , 1994 ) . Crossref, Google Scholar
G. Chen and X. Dong , From Chaos to Order ( World Scientific , Singapore , 1998 ) . Link, Google Scholar
A. L. Fradkov and A. Y. Pogromsky , Introduction to Control of Oscillations and Chaos ( World Scientific , Singapore , 1998 ) . Link, Google Scholar
P. Gahinet , A. Nemirovski and A. J. Laub , LMI Control Toolbox ( MathWorks, Inc. , Natick, MA , 1995 ) . Google Scholar
Hikihara, T. & Yamasue, K. [2002] "Domain of attraction for initial function space towards convergent solution in Duffing system under time-delayed feedback control," Technical Report of IEICE, NLP2002-50, 7–12 (in Japanese) . Google Scholar
S. Iplikci and Y. Denizhan, Chaos 12, 995 (2002). Crossref, Web of Science, Google Scholar
M. Ishii, K. Konishi and H. Kokame, Phys. Lett. A235, 603 (1997). Google Scholar
W. Justet al., Phys. Rev. Lett. 254, 158 (1999). Crossref, Web of Science, Google Scholar
H. K. Khalil , Nonlinear Systems ( Macmillan Publishing , NY , 2002 ) . Google Scholar
H. Kokameet al., Int. J. Contr. 74, 537 (2001). Crossref, Web of Science, Google Scholar
K. Konishi and H. Kokame, Phys. Lett. A248, 359 (1998). Google Scholar
K. Konishi, M. Ishii and H. Kokame, IEEE Trans. Circuits Syst.-I 46, 1285 (1999). Crossref, Web of Science, Google Scholar
H. Nakajima and Y. Ueda, Physica D111, 143 (1998). Google Scholar
H. Nakajima and Y. Ueda, Phys. Rev. E58, 1757 (1998). Google Scholar
E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990). Crossref, Web of Science, Google Scholar
K. Pyragas, Phys. Lett. A170, 421 (1992). Google Scholar
K. Pyragas, Phys. Lett. A206, 323 (1995). Google Scholar
K. Pyragas, Phys. Rev. Lett. 86, 2265 (2001). Crossref, Web of Science, Google Scholar
H. G. Schuster and M. B. Stemmler, Phys. Rev. E56, 6410 (1997). Google Scholar
H. G. Schuster , Handbook of Chaos Control ( Wiley-VCH , 1999 ) . Crossref, Google Scholar
T. Shinbrotet al., Phys. Rev. Lett. 65, 3215 (1990). Crossref, Web of Science, Google Scholar
J. A. K. Suykens, P. F. Curran and L. O. Chua, IEEE Trans. Circuits Syst.-I 46, 841 (1999). Crossref, Web of Science, Google Scholar
J. A. K. Suykens, B. L. R. De Moor and J. Vandewalle, IEEE Trans. Neural Networks 11, 222 (2000). Crossref, Web of Science, Google Scholar
T. Ushio, IEEE Trans. Circuits and Syst.-I 43, 815 (1996). Crossref, Web of Science, Google Scholar
S. Yamamoto, T. Hino and T. Ushio, IEEE Trans. Circuits Syst.-I 48, 785 (2001). Crossref, Web of Science, Google Scholar