A projection approach to H∞ control of time-delay systems

Vladimr Suplin; Emilia Fridman; Uri Shaked

doi:10.1109/CDC.2004.1429500

A projection approach to H_∞ control of time-delay systems

Vladimr Suplin^*, Emilia Fridman, Uri Shaked

^*Corresponding author for this work

School of Electrical Engineering

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

26 Scopus citations

Abstract

The issues of stability and H_∞ control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finsler's projection lemma, delay-dependent sufficient conditions are obtained, in terms of Linear Matrix Inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H_∞ state-feedback control. In addition to the new perspective it gives to the problems of control of systems with time-delay, the new approach provides new degrees of freedom in the design stage. These degrees of freedom lead to results that are less conservative than those obtained by the descriptor approach for systems with parameter uncertainties.

Original language	English
Title of host publication	2004 43rd IEEE Conference on Decision and Control (CDC)
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4548-4553
Number of pages	6
ISBN (Print)	0780386825
DOIs	https://doi.org/10.1109/CDC.2004.1429500
State	Published - 2004
Event	2004 43rd IEEE Conference on Decision and Control (CDC) - Nassau, Bahamas Duration: 14 Dec 2004 → 17 Dec 2004

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	5
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2004 43rd IEEE Conference on Decision and Control (CDC)
Country/Territory	Bahamas
City	Nassau
Period	14/12/04 → 17/12/04

Keywords

Lyapunov-krasovskii approach
Neutral systems
Time-delay systems

Access to Document

10.1109/CDC.2004.1429500

Cite this

@inproceedings{7861c90a716d4e96aea235dfefd4df8b,

title = "A projection approach to H∞ control of time-delay systems",

abstract = "The issues of stability and H∞ control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finsler's projection lemma, delay-dependent sufficient conditions are obtained, in terms of Linear Matrix Inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H∞ state-feedback control. In addition to the new perspective it gives to the problems of control of systems with time-delay, the new approach provides new degrees of freedom in the design stage. These degrees of freedom lead to results that are less conservative than those obtained by the descriptor approach for systems with parameter uncertainties.",

keywords = "Lyapunov-krasovskii approach, Neutral systems, Time-delay systems",

author = "Vladimr Suplin and Emilia Fridman and Uri Shaked",

year = "2004",

doi = "10.1109/CDC.2004.1429500",

language = "אנגלית",

isbn = "0780386825",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4548--4553",

booktitle = "2004 43rd IEEE Conference on Decision and Control (CDC)",

address = "ארצות הברית",

note = "2004 43rd IEEE Conference on Decision and Control (CDC) ; Conference date: 14-12-2004 Through 17-12-2004",

}

Suplin, V, Fridman, E & Shaked, U 2004, A projection approach to H_∞ control of time-delay systems. in 2004 43rd IEEE Conference on Decision and Control (CDC)., FrA12.6, Proceedings of the IEEE Conference on Decision and Control, vol. 5, Institute of Electrical and Electronics Engineers Inc., pp. 4548-4553, 2004 43rd IEEE Conference on Decision and Control (CDC), Nassau, Bahamas, 14/12/04. https://doi.org/10.1109/CDC.2004.1429500

A projection approach to H_∞ control of time-delay systems. / Suplin, Vladimr; Fridman, Emilia ; Shaked, Uri.
2004 43rd IEEE Conference on Decision and Control (CDC). Institute of Electrical and Electronics Engineers Inc., 2004. p. 4548-4553 FrA12.6 (Proceedings of the IEEE Conference on Decision and Control; Vol. 5).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A projection approach to H∞ control of time-delay systems

AU - Suplin, Vladimr

AU - Fridman, Emilia

AU - Shaked, Uri

PY - 2004

Y1 - 2004

N2 - The issues of stability and H∞ control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finsler's projection lemma, delay-dependent sufficient conditions are obtained, in terms of Linear Matrix Inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H∞ state-feedback control. In addition to the new perspective it gives to the problems of control of systems with time-delay, the new approach provides new degrees of freedom in the design stage. These degrees of freedom lead to results that are less conservative than those obtained by the descriptor approach for systems with parameter uncertainties.

AB - The issues of stability and H∞ control of linear systems with time-varying delays are considered. Based on the Lyapunov-Krasovskii approach and on Finsler's projection lemma, delay-dependent sufficient conditions are obtained, in terms of Linear Matrix Inequalities (LMIs), for the stability of these systems. These conditions generalize previous results that were derived using either the descriptor approach or the first and the third model transformations. The obtained criteria are extended to deal with: stabilizability, the bounded real lemma and the H∞ state-feedback control. In addition to the new perspective it gives to the problems of control of systems with time-delay, the new approach provides new degrees of freedom in the design stage. These degrees of freedom lead to results that are less conservative than those obtained by the descriptor approach for systems with parameter uncertainties.

KW - Lyapunov-krasovskii approach

KW - Neutral systems

KW - Time-delay systems

UR - http://www.scopus.com/inward/record.url?scp=14544301096&partnerID=8YFLogxK

U2 - 10.1109/CDC.2004.1429500

DO - 10.1109/CDC.2004.1429500

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:14544301096

SN - 0780386825

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4548

EP - 4553

BT - 2004 43rd IEEE Conference on Decision and Control (CDC)

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2004 43rd IEEE Conference on Decision and Control (CDC)

Y2 - 14 December 2004 through 17 December 2004

ER -