Bounded real criteria for linear time-delay systems

U. Shaked; I. Yaesh; C. E. De Souza

doi:10.1109/9.701117

Bounded real criteria for linear time-delay systems

U. Shaked^*, I. Yaesh, C. E. De Souza

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

79 Scopus citations

Abstract

This paper considers the problem of finding the H_∞-norm of a linear time-varying system having a delayed state and with an output that comprises a linear combination of the "current" state as well as of the "delayed" state. Both delay-independent and delay-dependent bounded real criteria are derived which provide sufficient conditions for the system to possess an H_∞-norm which is less than or equal to a prescribed bound. The stationary case for time-invariant systems is also tackled, and in this situation the proposed bounded real criteria are given in terms of linear matrix inequalities. Two examples are presented which compare the guaranteed bounds that are achieved by our results with the actual H_∞-norm of the system.

Original language	English
Pages (from-to)	1016-1022
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	43
Issue number	7
DOIs	https://doi.org/10.1109/9.701117
State	Published - 1998

Keywords

Bounded real lemma
H
Time-delay systems

Access to Document

10.1109/9.701117

Cite this

@article{57f8a845b08a4f149598aa0d7a0a9c6e,

title = "Bounded real criteria for linear time-delay systems",

abstract = "This paper considers the problem of finding the H∞-norm of a linear time-varying system having a delayed state and with an output that comprises a linear combination of the {"}current{"} state as well as of the {"}delayed{"} state. Both delay-independent and delay-dependent bounded real criteria are derived which provide sufficient conditions for the system to possess an H∞-norm which is less than or equal to a prescribed bound. The stationary case for time-invariant systems is also tackled, and in this situation the proposed bounded real criteria are given in terms of linear matrix inequalities. Two examples are presented which compare the guaranteed bounds that are achieved by our results with the actual H∞-norm of the system.",

keywords = "Bounded real lemma, H, Time-delay systems",

author = "U. Shaked and I. Yaesh and {De Souza}, {C. E.}",

note = "Funding Information: Manuscript received January 4, 1996; revised July 29, 1996. This work was supported by the Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico-CNPq, Brazil, under Grant 301653/96-8/NV/PQ. U. Shaked is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Tel-Aviv 69978, Israel. I. Yaesh is with Israel Military Industries, Advanced Systems Div., Ramat Hasharon, Israel. C. E. de Souza is with the Department of Systems and Control, Lab. Nacional de Computacao Cientifica-LNCC/CNPq, Petropolis, Rio de Janiero, Brazil. Publisher Item Identifier S 0018-9286(98)03596-X.",

year = "1998",

doi = "10.1109/9.701117",

language = "אנגלית",

volume = "43",

pages = "1016--1022",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

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

number = "7",

}

TY - JOUR

T1 - Bounded real criteria for linear time-delay systems

AU - Shaked, U.

AU - Yaesh, I.

AU - De Souza, C. E.

N1 - Funding Information: Manuscript received January 4, 1996; revised July 29, 1996. This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, Brazil, under Grant 301653/96-8/NV/PQ. U. Shaked is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Tel-Aviv 69978, Israel. I. Yaesh is with Israel Military Industries, Advanced Systems Div., Ramat Hasharon, Israel. C. E. de Souza is with the Department of Systems and Control, Lab. Nacional de Computacao Cientifica-LNCC/CNPq, Petropolis, Rio de Janiero, Brazil. Publisher Item Identifier S 0018-9286(98)03596-X.

PY - 1998

Y1 - 1998

N2 - This paper considers the problem of finding the H∞-norm of a linear time-varying system having a delayed state and with an output that comprises a linear combination of the "current" state as well as of the "delayed" state. Both delay-independent and delay-dependent bounded real criteria are derived which provide sufficient conditions for the system to possess an H∞-norm which is less than or equal to a prescribed bound. The stationary case for time-invariant systems is also tackled, and in this situation the proposed bounded real criteria are given in terms of linear matrix inequalities. Two examples are presented which compare the guaranteed bounds that are achieved by our results with the actual H∞-norm of the system.

AB - This paper considers the problem of finding the H∞-norm of a linear time-varying system having a delayed state and with an output that comprises a linear combination of the "current" state as well as of the "delayed" state. Both delay-independent and delay-dependent bounded real criteria are derived which provide sufficient conditions for the system to possess an H∞-norm which is less than or equal to a prescribed bound. The stationary case for time-invariant systems is also tackled, and in this situation the proposed bounded real criteria are given in terms of linear matrix inequalities. Two examples are presented which compare the guaranteed bounds that are achieved by our results with the actual H∞-norm of the system.

KW - Bounded real lemma

KW - H

KW - Time-delay systems

UR - http://www.scopus.com/inward/record.url?scp=0032123743&partnerID=8YFLogxK

U2 - 10.1109/9.701117

DO - 10.1109/9.701117

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0032123743

SN - 0018-9286

VL - 43

SP - 1016

EP - 1022

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 7

ER -

Bounded real criteria for linear time-delay systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this