A stability result for delayed feedback controllers

Date
2003
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Source Title
Proceedings of the 42nd IEEE International Conference on Decision and Control, IEEE 2003
Print ISSN
0191-2216
Electronic ISSN
Publisher
IEEE
Volume
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Pages
1889 - 1894
Language
English
Type
Conference Paper
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Abstract

We consider the delayed feedback control (DFC) scheme for one dimensional discrete time systems. To analyze the stability, we construct a map whose fixed points correspond to the periodic orbits of the system to be controlled. Then the stability of the DFC is equivalent to the stability of the corresponding equilibrium point of the constructed map. We obtain a formula for the characteristic polynomial of the Jacobian of this map. Then the Schur stability of this polynomial could be used to analyze the stability of DFC. We also present some simulation results.

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Keywords
Chaos control, Delayed feedback system, Pyragas controller, Stability, Chaos theory, Computer simulation, Discrete time control systems, Mathematical models, Polynomials, Delayed feedback control (DFC), Feedback control
Citation
Published Version (Please cite this version)