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 - 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

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10.1016/S1474-6670(17)33298-6

Cite this

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title = "Delayed feedback control of linear systems with state jump",

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.",

keywords = "Operators, Periodic motion, Stability analysis, Time-delay, Walking",

author = "Kentaro Hirata and Hideki Kokame",

note = "Publisher Copyright: {\textcopyright} 2003 IFAC.; 4th IFAC Workshop on Time Delay Systems, TDS 2003 ; Conference date: 08-09-2003 Through 10-09-2003",

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doi = "10.1016/S1474-6670(17)33298-6",

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TY - JOUR

T1 - Delayed feedback control of linear systems with state jump

AU - Hirata, Kentaro

AU - Kokame, Hideki

PY - 2003

Y1 - 2003

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

UR - http://www.scopus.com/inward/record.url?scp=80051535763&partnerID=8YFLogxK

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U2 - 10.1016/S1474-6670(17)33298-6

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

M3 - Conference article

AN - SCOPUS:80051535763

VL - 36

SP - 35

EP - 40

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 19

T2 - 4th IFAC Workshop on Time Delay Systems, TDS 2003

Y2 - 8 September 2003 through 10 September 2003

ER -

Delayed feedback control of linear systems with state jump

Abstract

Keywords

ASJC Scopus subject areas

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