Delayed feedback control of linear systems with state jump

Kentaro Hirata; Hideki Kokame

doi:10.1016/S1474-6670(17)33298-6

Delayed feedback control of linear systems with state jump

Kentaro Hirata, Hideki Kokame

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

The effect of the delayed feedback control on the stability of periodic solutions of linear systems with sate jump is examined. Although the stability of the open-loop and the OGY feedback cases can be analyzed via matrix representations (Poincare map), the system with DFC requires an operator representation of the state transition on a certain function space due to the infinitedimensionality caused by the time delay element in the controller. A stability condition is given in terms of the spectrum of this operator. Also an analytic formula and a numerical method for the computation of the spectrum are provided.

Original language	English
Pages (from-to)	35-40
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	36
Issue number	19
DOIs	https://doi.org/10.1016/S1474-6670(17)33298-6
Publication status	Published - Jan 1 2003
Externally published	Yes
Event	4th IFAC Workshop on Time Delay Systems, TDS 2003 - Rocquencourt, France Duration: Sep 8 2003 → Sep 10 2003

Keywords

Operators
Periodic motion
Stability analysis
Time-delay
Walking

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1016/S1474-6670(17)33298-6

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abstract = "The effect of the delayed feedback control on the stability of periodic solutions of linear systems with sate jump is examined. Although the stability of the open-loop and the OGY feedback cases can be analyzed via matrix representations (Poincare map), the system with DFC requires an operator representation of the state transition on a certain function space due to the infinitedimensionality caused by the time delay element in the controller. A stability condition is given in terms of the spectrum of this operator. Also an analytic formula and a numerical method for the computation of the spectrum are provided.",

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T1 - Delayed feedback control of linear systems with state jump

AU - Hirata, Kentaro

AU - Kokame, Hideki

PY - 2003/1/1

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N2 - The effect of the delayed feedback control on the stability of periodic solutions of linear systems with sate jump is examined. Although the stability of the open-loop and the OGY feedback cases can be analyzed via matrix representations (Poincare map), the system with DFC requires an operator representation of the state transition on a certain function space due to the infinitedimensionality caused by the time delay element in the controller. A stability condition is given in terms of the spectrum of this operator. Also an analytic formula and a numerical method for the computation of the spectrum are provided.

AB - The effect of the delayed feedback control on the stability of periodic solutions of linear systems with sate jump is examined. Although the stability of the open-loop and the OGY feedback cases can be analyzed via matrix representations (Poincare map), the system with DFC requires an operator representation of the state transition on a certain function space due to the infinitedimensionality caused by the time delay element in the controller. A stability condition is given in terms of the spectrum of this operator. Also an analytic formula and a numerical method for the computation of the spectrum are provided.

KW - Operators

KW - Periodic motion

KW - Stability analysis

KW - Time-delay

KW - Walking

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DO - 10.1016/S1474-6670(17)33298-6

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SP - 35

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JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

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