H−/H∞ fault detection filter design for discrete-time Takagi–Sugeno fuzzy system

In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable. The idea is to formulate the robu...

Full description

Saved in:
Bibliographic Details
Published inAutomatica (Oxford) Vol. 49; no. 7; pp. 1996 - 2005
Main Authors Chadli, Mohammed, Abdo, Ali, Ding, Steven X.
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.07.2013
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Descriptor observer
Disturbance
Exact sciences and technology
Fault detection
formula omitted
Modelling and identification
T–S fuzzy models
H
LMI
Fault detection
T–S fuzzy models
Descriptor observer
Disturbance
Disturbance rejection
Descriptor system
LMl
Modeling
Robust control
Fuzzy logic
Discrete filter
Observer
Discrete time
T―S fuzzy models
Linear matrix inequality
System identification
Auxiliary variable
Fault diagnostic
Measurement error
Defect detection
Lyapunov function
Online AccessGet full text
ISSN0005-1098
1873-2836
DOI10.1016/j.automatica.2013.03.014

Cover

Abstract In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable. The idea is to formulate the robust fault detection observer design as an H−/H∞ problem. Based on nonquadratic Lyapunov functions, a solution of the considered problem is then given via a Linear Matrix Inequality (LMI) formulation. An example is proposed to illustrate the design conditions.
AbstractList In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable. The idea is to formulate the robust fault detection observer design as an H−/H∞ problem. Based on nonquadratic Lyapunov functions, a solution of the considered problem is then given via a Linear Matrix Inequality (LMI) formulation. An example is proposed to illustrate the design conditions.
Author Abdo, Ali
Chadli, Mohammed
Ding, Steven X.
Author_xml – sequence: 1
  givenname: Mohammed
  surname: Chadli
  fullname: Chadli, Mohammed
  email: mchadli@u-picardie.fr, chadli@ieee.org
  organization: University of Picardie Jules Verne-MIS (E.A. 4290), 33 rue Saint-Leu, 80039, Amiens, France
– sequence: 2
  givenname: Ali
  surname: Abdo
  fullname: Abdo, Ali
  email: ali.abdo@uni-due.de
  organization: University of Duisburg-Essen, Bismarkstrasse 81 BB, 47057 Duisburg, Germany
– sequence: 3
  givenname: Steven X.
  surname: Ding
  fullname: Ding, Steven X.
  email: steven.ding@uni-due.de
  organization: University of Duisburg-Essen, Bismarkstrasse 81 BB, 47057 Duisburg, Germany
BackLink http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=27469206$$DView record in Pascal Francis
BookMark eNpFUMtKA0EQHCSCSfQf9uJxk3ntY44a1AgBD0avQ2e2N0zcR9iZFZKTR8969-PyJU6IIDTdXd1FU10jMmjaBgmJGJ0wytLpZgK9b2vw1sCEUyYmNASTZ2TI8kzEPBfpgAwppUnMqMovyMi5TYCS5XxIXueHz69pSD9RCX3lowI9Gm_bJipt5bELA2fXAbWhtc50YR97W2O0hDdY28PH93O_xqaNyn6_30Vu5zzWl-S8hMrh1V8dk5f7u-VsHi-eHh5nN4sYWaJ8LEu2CpJBJcZAydMSM6XYilGZJ8IAZsiwYLkBwXnOeVZQKgC5kqgSCTIVY3J9ursFZ6AqO2iMdXrb2Rq6neaZTBWnR97tiYdBzLvFTjtjsTFY2C68q4vWakb10VG90f-O6qOjmoZgUvwC_fFzGg
CODEN ATCAA9
ContentType Journal Article
Copyright 2013 Elsevier Ltd
2014 INIST-CNRS
Copyright_xml – notice: 2013 Elsevier Ltd
– notice: 2014 INIST-CNRS
DBID IQODW
DOI 10.1016/j.automatica.2013.03.014
DatabaseName Pascal-Francis
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Applied Sciences
EISSN 1873-2836
EndPage 2005
ExternalDocumentID 27469206
S0005109813001830
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
1B1
1~.
1~5
23N
3R3
4.4
457
4G.
5GY
5VS
6TJ
7-5
71M
8P~
9JN
9JO
AAAKF
AAAKG
AABNK
AACTN
AAEDT
AAEDW
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXUO
ABDEX
ABFNM
ABFRF
ABJNI
ABMAC
ABUCO
ABXDB
ABYKQ
ACBEA
ACDAQ
ACGFO
ACGFS
ACNNM
ACRLP
ADBBV
ADEZE
ADIYS
ADMUD
ADTZH
AEBSH
AECPX
AEFWE
AEKER
AENEX
AFFNX
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHJVU
AHPGS
AI.
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
APLSM
ASPBG
AVWKF
AXJTR
AZFZN
BJAXD
BKOJK
BLXMC
CS3
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HAMUX
HLZ
HVGLF
HZ~
H~9
IHE
J1W
JJJVA
K-O
KOM
LG9
LY7
M41
MO0
N9A
O-L
O9-
OAUVE
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
RXW
SBC
SDF
SDG
SDP
SES
SET
SEW
SPC
SPCBC
SSB
SSD
SST
SSZ
T5K
T9H
TAE
TN5
VH1
WH7
WUQ
X6Y
XFK
XPP
ZMT
~G-
AATTM
AAXKI
ABWVN
ACRPL
ADNMO
AEIPS
AFJKZ
AKRWK
ANKPU
BNPGV
IQODW
SSH
ID FETCH-LOGICAL-e159t-4f1b013a95ccaf26fe7991b104853cae7e1ed18ca3228227d003ae294e954a463
IEDL.DBID AIKHN
ISSN 0005-1098
IngestDate Wed Apr 02 07:49:42 EDT 2025
Fri Feb 23 02:14:09 EST 2024
IsPeerReviewed true
IsScholarly true
Issue 7
Keywords H
LMI
Fault detection
T–S fuzzy models
Descriptor observer
Disturbance
Disturbance rejection
Descriptor system
LMl
Modeling
Robust control
Fuzzy logic
Discrete filter
Observer
Discrete time
T―S fuzzy models
Linear matrix inequality
System identification
Auxiliary variable
Fault diagnostic
Measurement error
Defect detection
Lyapunov function
Language English
License CC BY 4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-e159t-4f1b013a95ccaf26fe7991b104853cae7e1ed18ca3228227d003ae294e954a463
PageCount 10
ParticipantIDs pascalfrancis_primary_27469206
elsevier_sciencedirect_doi_10_1016_j_automatica_2013_03_014
PublicationCentury 2000
PublicationDate 2013-07-00
PublicationDateYYYYMMDD 2013-07-01
PublicationDate_xml – month: 07
  year: 2013
  text: 2013-07-00
PublicationDecade 2010
PublicationPlace Kidlington
PublicationPlace_xml – name: Kidlington
PublicationTitle Automatica (Oxford)
PublicationYear 2013
Publisher Elsevier Ltd
Elsevier
Publisher_xml – name: Elsevier Ltd
– name: Elsevier
References Gao, Z., Shi, X., & Ding, S. X. (2005). Observer design for T–S fuzzy systems with measurement output noises. In
Johansson, Bask, Norlander (br000105) 2006; 42
Beijing.
Patton, J., Chen, J., & Lobez-Toribio, J. (1998). Fuzzy observer for non-linear dynamic system fault diagnosis. In
Alcorta, E., & Sauceda, S. (2003). Fault detection and isolation based on Takagi–Sugeno modeling. In
Dalton, T., & Frank, P. M. (1999). Application of fuzzy logic based methods of residual evaluation to the three tank benchmark. In
Guoa, Huang, Cui (br000090) 2009; 57
Wang, H., Wang, J., Liu, J., & Lam, J. (2003). Iterative LMI approach for robust fault detection observer design. In
Ding, S. X., Zhang, P., Frank, P. M., & Ding, E. L. (2003). Threshold calculation using LMI-technique and its integration in the design of fault detection systems. In
Bouattour, Chadli, Chaabane, El Hajjaji (br000015) 2011; 9
Chadli, Karimi (br000030) 2013; 21
Frank, P. M., Ding, S. X., & Koppen-Seliger, B. (2000). Current developments in the theory of FDI. In
Frank, Ding, Marcu (br000065) 2000; 22
Tuan, Apkarian, Narikiyo, Yamamoto (br000130) 2001; 9
Prague, Czech Republic.
Wang, Yang, Liu (br000140) 2007; 43
Gertler (br000085) 1998
Boyd, El Ghaoui, Feron, Balakrishnan (br000020) 1994
Nguang, Shi, Ding (br000115) 2007; 15
Chadli, Akhenak, Ragot, Maquin (br000025) 2009; 346
Gao, Shi, Ding (br000080) 2008; 38
Barcelona.
El-Ghatwary, M.G., Ding, S. X., & Gao, Z. (2006). Robust fault detection for uncertain Takagi–Sugeno fuzzy systems with parametric uncertainty and process disturbances. In
(pp. 84–89). USA.
Gao, Ding (br000070) 2007; 43
Chen, Patton (br000035) 1999
Budapest, August 23–26.
(pp. 673–678). USA.
.
Abid, M., Ding, S. X., & Kahn, A. Q. (2009). Dynamic threshold for fault detection in Lipschitz nonlinear systems. In
Isermann (br000095) 1997; 5
Ding (br000045) 2008
Liu, Wang, Yang (br000110) 2005; 41
Zhong, Ding, Lam, Wang (br000145) 2003; 39
Takagi, Sugeno (br000125) 1985; 15
Maui, Hawaii, USA.
Jaimoukha, Li (br000100) 2006; 42
References_xml – reference: (pp. 673–678). USA.
– year: 1998
  ident: br000085
  article-title: Fault detection and diagnosis in engineering systems
– volume: 43
  start-page: 912
  year: 2007
  end-page: 920
  ident: br000070
  article-title: Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems
  publication-title: Automatica
– volume: 57
  start-page: 1743
  year: 2009
  end-page: 1747
  ident: br000090
  article-title: Design and analysis of robust fault detection filter using LMI tools
  publication-title: Computers and Mathematics with Applications
– volume: 42
  start-page: 1907
  year: 2006
  end-page: 1912
  ident: br000100
  article-title: A matrix factorization solution to the
  publication-title: Automatica
– volume: 9
  start-page: 324
  year: 2001
  end-page: 332
  ident: br000130
  article-title: Parameterized linear matrix inequality techniques in fuzzy control system design
  publication-title: IEEE Transactions on Fuzzy Systems
– reference: Abid, M., Ding, S. X., & Kahn, A. Q. (2009). Dynamic threshold for fault detection in Lipschitz nonlinear systems. In
– reference: . Budapest, August 23–26.
– volume: 9
  start-page: 973
  year: 2011
  end-page: 979
  ident: br000015
  article-title: Design of robust fault detection observer for Takagi–Sugeno models using the descriptor approach
  publication-title: International Journal of Control, Automation and Systems
– volume: 15
  start-page: 116
  year: 1985
  end-page: 132
  ident: br000125
  article-title: Fuzzy identification of systems and its applications to modeling and control
  publication-title: IEEE Transactions on Systems, Man, and Cybernetics
– reference: Gao, Z., Shi, X., & Ding, S. X. (2005). Observer design for T–S fuzzy systems with measurement output noises. In
– reference: (pp. 84–89). USA.
– volume: 38
  year: 2008
  ident: br000080
  article-title: Fuzzy state-disturbance observer design for T–S fuzzy systems with application to sensor fault estimation
  publication-title: IEEE Transactions on Systems, Man, and Cybernetics, Part B
– year: 1994
  ident: br000020
  article-title: Linear matrix inequalities in system and control theory
– reference: Ding, S. X., Zhang, P., Frank, P. M., & Ding, E. L. (2003). Threshold calculation using LMI-technique and its integration in the design of fault detection systems. In
– volume: 42
  start-page: 1095
  year: 2006
  end-page: 1106
  ident: br000105
  article-title: Dynamic threshold generators for robust fault detection in linear systems with parameter uncertainty
  publication-title: Automatica
– reference: . Beijing.
– volume: 39
  start-page: 543
  year: 2003
  end-page: 550
  ident: br000145
  article-title: An LMI approach to design robust fault detection Filter for uncertain LTI systems
  publication-title: Automatica
– reference: Frank, P. M., Ding, S. X., & Koppen-Seliger, B. (2000). Current developments in the theory of FDI. In
– reference: Wang, H., Wang, J., Liu, J., & Lam, J. (2003). Iterative LMI approach for robust fault detection observer design. In
– reference: . Prague, Czech Republic.
– year: 1999
  ident: br000035
  article-title: Model based fault diagnosis for dynamic systems
– volume: 43
  start-page: 1656
  year: 2007
  end-page: 1665
  ident: br000140
  article-title: An LMI approach to
  publication-title: Automatica
– reference: El-Ghatwary, M.G., Ding, S. X., & Gao, Z. (2006). Robust fault detection for uncertain Takagi–Sugeno fuzzy systems with parametric uncertainty and process disturbances. In
– reference: Patton, J., Chen, J., & Lobez-Toribio, J. (1998). Fuzzy observer for non-linear dynamic system fault diagnosis. In
– reference: .
– reference: Dalton, T., & Frank, P. M. (1999). Application of fuzzy logic based methods of residual evaluation to the three tank benchmark. In
– year: 2008
  ident: br000045
  article-title: Model based faults diagnosis techniques-design schemes, algorithms and tools
– volume: 41
  start-page: 1995
  year: 2005
  end-page: 2004
  ident: br000110
  article-title: An LMI approach to minimum sensitivity analysis with application to fault detection
  publication-title: Automatica
– volume: 21
  start-page: 158
  year: 2013
  end-page: 164
  ident: br000030
  article-title: Robust observer design for unknown inputs Takagi–Sugeno models
  publication-title: IEEE Transactions on Fuzzy Systems
– volume: 346
  start-page: 593
  year: 2009
  end-page: 610
  ident: br000025
  article-title: State and unknown input estimation for discrete time multiple model
  publication-title: Journal of the Franklin Institute
– volume: 22
  start-page: 57
  year: 2000
  end-page: 101
  ident: br000065
  article-title: Model based fault diagnosis in technical processes
  publication-title: Transactions of the Institute of Measurements and Control
– reference: . Maui, Hawaii, USA.
– reference: Alcorta, E., & Sauceda, S. (2003). Fault detection and isolation based on Takagi–Sugeno modeling. In
– volume: 5
  start-page: 259
  year: 1997
  end-page: 285
  ident: br000095
  article-title: Fault detection and fault diagnosis methods
  publication-title: Control Engineering Practice
– volume: 15
  year: 2007
  ident: br000115
  article-title: Fault detection for uncertain fuzzy systems: an LMI approach
  publication-title: IEEE Transactions on Fuzzy Systems
– reference: . Barcelona.
SSID ssj0004182
Score 2.5669513
Snippet In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The...
SourceID pascalfrancis
elsevier
SourceType Index Database
Publisher
StartPage 1996
SubjectTerms Applied sciences
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Descriptor observer
Disturbance
Exact sciences and technology
Fault detection
formula omitted
Modelling and identification
T–S fuzzy models
Title H−/H∞ fault detection filter design for discrete-time Takagi–Sugeno fuzzy system
URI https://dx.doi.org/10.1016/j.automatica.2013.03.014
Volume 49
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV09T8MwELVKu4AQ4lOUj8oDa2jtOG4spqqiCiC60KJukZPYKIDSqiQDHRAjM-z8uP4SzkmqtjNSlMGRouidffcc371D6ALMSgMpIstmQWAxIPyWYFpZitihloLrMG_Ted_n3pDdjpxRBXUXtTAmrbL0_YVPz711OdIs0WxO4tjU-JoJJVxzIAMTE_btNWoL7lRRrXNz5_WX5ZHELUTDc9FN4ZYJPUWal8zScS6OakSIiJ0rnpqSnpXQtD2RbwCYLjpdrISf3i7aKXkj7hSftocqKtlHWytqggfo0Zt_fTfh9ou1zF5THKk0T7RKsI7NoTgMmHQNDDwVm2rcKTy3THN5PJAv8imef_48ZEa0FetsNnvHhcrzIRr2rgddzyrbJgDAjkgtpon5uSmFA9bRlGvVBhIYgBkgNIdStRVREXFDCWsZ6EE7goUtFRVMCYdJxu0jVE3GiToGmBwN-0clNGUQxVoayCKnKpIApQ5cN6ijqwVM_prVfHDI_iKB7NlfguwbkP0WXITVUWMNWX9SCGz4sFPmgrb4yb9ef4o2ad67wuTWnqFqOs3UOTCINGigjcsP0ijnyR9A4MoN
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELaqMgBCiKcoj-KBNbRJnIfFhCqqAG0XWtTNchIbBVBalWSgA2Jkhp0f11_C2UnVdkaKMjhSFH1n353j775D6ALMaoWcxoZNwtAgkPAblEhhCNOOJKeujHSbzm7PDQbkbugMK6g1r4VRtMrS9xc-XXvrcqRRotkYJ4mq8VUTivrqQAYmJuzb14hje4rXd_mx4HkQ0y8kw7XkJvVLOk9B8uJ5NtLSqEqCyLS13qkq6FkKTFtj_gZwyaLPxVLwae-g7TJrxNfFh-2iikj30OaSluA-egxmX98NuP1iyfPXDMci0zSrFMtEHYnDgCJrYMhSsarFncBzQ7WWx33-wp-S2efPQ64kW7HMp9N3XGg8H6BB-6bfCoyyaQLA69DMINJUvzY5dcA20nKl8CAFDMEIEJgjLjxhitj0Iw4rGZIDL4ZlzYVFiaAO4cS1D1E1HaXiCGByJOweBZUWgRjWlJAqupaIOUApQ98Pa-hqDhNbsRkDd8zm9LFntgCZKZBZEy6T1FB9BVk2LuQ1GOyTXWo13eN_vf4crQf9bod1bnv3J2jD0l0sFMv2FFWzSS7OIJfIwrqeK3_4hMrY
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=H%E2%88%92%2FH%E2%88%9E+fault+detection+filter+design+for+discrete-time+Takagi%E2%80%93Sugeno+fuzzy+system&rft.jtitle=Automatica+%28Oxford%29&rft.au=Chadli%2C+Mohammed&rft.au=Abdo%2C+Ali&rft.au=Ding%2C+Steven+X.&rft.date=2013-07-01&rft.pub=Elsevier+Ltd&rft.issn=0005-1098&rft.eissn=1873-2836&rft.volume=49&rft.issue=7&rft.spage=1996&rft.epage=2005&rft_id=info:doi/10.1016%2Fj.automatica.2013.03.014&rft.externalDocID=S0005109813001830
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0005-1098&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0005-1098&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0005-1098&client=summon