International Journal of Robust and Nonlinear Control

Research Article

On relay feedback and chaotic systems

Corresponding Author

Akihiko Sugiki

[email protected]

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan===Search for more papers by this author

Shoshiro Hatakeyama,

Shoshiro Hatakeyama

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan

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Katsuhisa Furuta,

Katsuhisa Furuta

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan

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Akihiko Sugiki,

Corresponding Author

Akihiko Sugiki

[email protected]

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan===Search for more papers by this author

Shoshiro Hatakeyama,

Shoshiro Hatakeyama

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan

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Katsuhisa Furuta,

Katsuhisa Furuta

Department of Applied Systems Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Saitama, Japan

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First published: 06 March 2001

https://doi.org/10.1002/rnc.573

Citations: 4

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Abstract

The feedback connection of a linear system with a memoryless nonlinearity is recognized as a candidate for chaos-generating structure. This paper proposes a chaotic nonlinear feedback system with a relay connected to a biproper linear system. The proposed chaotic system is analysed using chaos criteria proposed by Genesio and Tesi. This paper also shows an equivalence relation between the proposed system and the Brockett chaotic system through the linear input–output transformation. Copyright © 2001 John Wiley & Sons, Ltd.

REFERENCES

1 Kalman RE. Nonlinear aspects of sampled-data control systems. Proceedings of the Symposium on Nonlinear Circuit Analysis 1956; 273–313.
Google Scholar
2 Brockett RW. On condition leading to chaos in feedback systems. Proceedings of the 21st IEEE Conference on Decision and Control 1982; 932–936.
Google Scholar
3 Baillieul J, Brockett RW, Washburn RB. Chaotic motion in nonlinear feedback systems. IEEE Transactions on Circuits and Systems 1980; 27(11): 990–997.
10.1109/TCS.1980.1084739
Web of Science® Google Scholar
4 Matsumoto T. Chaos in electric circuit. Proceedings of the IEEE 1987; 75(8): 1033–1057.
10.1109/PROC.1987.13848
Web of Science® Google Scholar
5 Vaněček A, C̆elikovský S. Chaos synthesis via root locus. IEEE Transactions on Circuits and Systems-I 1994; 41(1): 59–60.
10.1109/81.260222
Web of Science® Google Scholar
6 Amrani D, Atherton DP. Designing autonomous relay systems with chaotic motion. Proceedings of the 28st IEEE Conference on Decision and Control 1989; 512–517.
Google Scholar
7 Genesio R, Tesi A. Chaos prediction in nonlinear feedback system. IEE Proceedings-D 1991; 138(4): 313–320.
10.1049/ip-d.1991.0042
Web of Science® Google Scholar
8 Anishchenko VS. Dynamical Chaos — Models, Experiments, and Applications. World Scientific: Singapore, 1995.
Google Scholar
9 Okabayashi R, Furuta K. A note on sliding mode control systems from the viewpoint of the Lur'e problem. Transactions of the Society of Instrument and Control Engineers 1999; 35(4): 580–582.
10.9746/sicetr1965.35.580
Google Scholar
10 Genesio R, Tesi A. Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 1992; 28(3): 531–548.
10.1016/0005-1098(92)90177-H
Web of Science® Google Scholar
11 Sugiki A, Hatakeyama S, Furuta K. A chaos model via relay feedback. Proceedings of the IEEE Symposium on Computer Aided System Design 1999; 1389–1393.
Google Scholar
12 Genesio R, Tesi A. A harmonic balance approach for chaos prediction:Chua's circuit. International Journal of Bifurcation and Chaos 1992; 2(1): 61–79.
10.1142/S0218127492000070
Web of Science® Google Scholar

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Volume11, Issue3

Special Issue:Control of Oscillatory Systems

March 2001

Pages 241-252

On relay feedback and chaotic systems

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