Dynamic delayed feedback controllers for chaotic discrete-time systems

Author

Yamamoto, Shigeru ; Hino, Toru ; Ushio, Toshimitsu

Author_Institution

Dept. of Syst. & Human Sci., Osaka Univ., Japan

Volume

48

Issue

6

fYear

2001

fDate

6/1/2001 12:00:00 AM

Firstpage

785

Lastpage

789

Abstract

Delayed feedback control (DFC), proposed by Pyragas [1992], is one of the useful control methods for chaotic systems. However, this static DFC has a limitation such that it can not stabilize any systems with an odd number of real eigenvalues greater than unity. In this paper, to overcome the limitation we introduce dynamic delayed feedback, and derive a necessary and sufficient condition for stabilization of such chaotic systems. Moreover, it is shown that the order of the dynamic delayed feedback controller is not necessarily greater than that of the chaotic system. Furthermore, we show a method of designing reduced-order controllers which is based on the linear matrix inequalities

Keywords

chaos; discrete time systems; eigenvalues and eigenfunctions; feedback; nonlinear control systems; reduced order systems; stability; chaotic discrete-time systems; dynamic delayed feedback controllers; linear matrix inequalities; real eigenvalues; reduced-order controllers; stabilization; Adaptive control; Chaos; Control systems; Delay; Design methodology; Digital-to-frequency converters; Eigenvalues and eigenfunctions; Feedback control; Linear matrix inequalities; Sufficient conditions;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.928162

Filename

928162