This paper deals with the fault observer and fault-tolerant controller design for singular Takagi–Sugeno (T–S) fuzzy systems subject to actuator faults. First, a novel proportional-integral observer is constructed to estimate the system states and faults. Sufficient conditions for the existence of the proposed observer are given in linear matrix inequality (LMI) terms. Furthermore, based on the state and fault estimation (FE), a fault-tolerant controller (FTC) is designed to effectively accommodate the influence of fault upon state and ensure that the closed-loop system is stable. Finally, a numerical example is given to show the effectiveness of the presented method.

References

References
1.
Edwards
,
C.
,
Spurgeon
,
S. K.
, and
Patton
,
R. J.
,
2000
, “
Sliding Mode Observers for Fault Detection and Isolation
,”
Automatica
,
36
(
4
), pp.
541
553
.
2.
Su
,
X. J.
,
Liu
,
X. X.
, and
Song
,
Y. D.
,
2017
, “
Event-Triggered Sliding Mode Control for Multi-Area Power Systems
,”
IEEE Trans. Ind. Electron.
,
64
(
8
), pp.
6732
6741
.
3.
Koenig
,
D.
,
2005
, “
Unknown Input Proportional Multiple–Integral Observer Design for Linear Descriptor Systems: Application to State and Fault Estimation
,”
IEEE Trans. Autom. Control
,
50
(
2
), pp.
212
217
.
4.
Lee
,
D. J.
,
Park
,
Y.
, and
Park
,
Y.
,
2012
, “
Robust H∞ Sliding Mode Descriptor Observer for Fault and Output Disturbance Estimation of Uncertain Systems
,”
IEEE Trans. Autom. Control
,
57
(
11
), pp.
2928
2934
.
5.
Li
,
X. J.
, and
Yang
,
G. H.
,
2012
, “
Dynamic Observer-Based Robust Control and Fault Detection for Linear Systems
,”
IET Control Theory Appl.
,
6
(
17
), pp.
2657
2666
.
6.
Zhang
,
P.
,
Ding
,
S. X.
, and
Liu
,
P.
,
2012
, “
A Lifting Based Approach to Observer Based Fault Detection of Linear Periodic Systems
,”
IEEE Trans. Autom. Control
,
57
(
2
), pp.
457
462
.
7.
Nguang
,
S.
,
Shi
,
P.
, and
Ding
,
S.
,
2007
, “
Fault Detection for Uncertain Fuzzy Systems: An LMI Approach
,”
IEEE Trans. Fuzzy Syst.
,
15
(
6
), pp.
1251
1262
.
8.
Cao
,
Y. Y.
, and
Frank
,
P. M.
,
2001
, “
Stability Analysis and Synthesis of Nonlinear Time-Delay Systems Via Linear Takagi–Sugeno Fuzzy Models
,”
Fuzzy Sets Syst.
,
124
(
2
), pp.
213
229
.
9.
Wu
,
L.
, and
Ho
,
D. W. C.
,
2009
, “
Fuzzy Filter Design for Nonlinear Itô Stochastic Systems With Application to Sensor Fault Detection
,”
IEEE Trans. Fuzzy Syst.
,
17
(
1
), pp.
233
242
.
10.
Zhang
,
K.
,
Jiang
,
B.
, and
Staroswiecki
,
M.
,
2010
, “
Dynamic Output Feedback Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Systems With Actuator Faults
,”
IEEE Trans. Fuzzy Syst.
,
18
(
1
), pp.
194
201
.
11.
Zhang
,
K.
,
Jiang
,
B.
, and
Shi
,
P.
,
2015
, “
Analysis and Design of Robust H∞ Fault Estimation Observer With Finite-Frequency Specifications for Discrete-Time Fuzzy Systems
,”
IEEE Trans. Cybern.
,
45
(
7
), pp.
1225
1235
.
12.
Dong
,
J. X.
, and
Hou
,
J. T.
,
2017
, “
Output Feedback Fault-Tolerant Control by a Set-Theoretic Description of T–S Fuzzy Systems
,”
Appl. Math. Comput.
,
301
, pp.
117
134
.
13.
Jia
,
Q. X.
,
Chen
,
W.
, and
Wang
,
P.
,
2017
, “
Design of a PD-Type Learning Observer for Reconstruction of Actuator Faults in Descriptor Systems
,”
IET Control Theory Appl.
,
11
(
1
), pp.
17
24
.
14.
Shen
,
Q. K.
,
Jiang
,
B.
, and
Cocquempot
,
V.
,
2012
, “
Fault Tolerant Control for T–S Fuzzy Systems With Application to Near-Space Hypersonic Vehicle With Actuator Faults
,”
IEEE Trans. Fuzzy Syst.
,
20
(
4
), pp.
652
665
.
15.
Shen
,
Q. K.
,
Jiang
,
B.
, and
Cocquempot
,
V.
,
2013
, “
Fuzzy Logic System-Based Adaptive Fault Tolerant Control for Near-Space Vehicle Attitude Dynamics With Actuator Faults
,”
IEEE Trans. Fuzzy Syst.
,
21
(
2
), pp.
289
300
.
16.
Li
,
X. H.
,
Zhu
,
F. L.
, and
Chakrabarty
,
A.
,
2016
, “
Nonfragile Fault Tolerant Fuzzy Observer-Based Controller Design for Nonlinear Systems
,”
IEEE Trans. Fuzzy Syst.
,
24
(
6
), pp.
1679
1689
.
17.
Huang
,
S. J.
, and
Yang
,
G. H.
,
2014
, “
Fault Tolerant Controller Design for T–S Fuzzy Systems With Time-Varying Delay and Actuator Faults: A K-Step Fault-Estimation Approach
,”
IEEE Trans. Fuzzy Syst.
,
22
(
6
), pp.
1526
1540
.
18.
Chadli
,
M.
,
Abdo
,
A.
, and
Ding
,
S. X.
,
2013
, “
H2/H∞ Fault Detection Filter Design for Discrete-Time Takagi–Sugeno Fuzzy System
,”
Automatica
,
49
(
7
), pp.
1996
2005
.
19.
Liu
,
M.
,
Cao
,
X. B.
, and
Shi
,
P.
,
2013
, “
Fault Estimation and Tolerant Control for Fuzzy Stochastic Systems
,”
IEEE Trans. Fuzzy Syst.
,
21
(
2
), pp.
221
229
.
20.
Liu
,
M.
,
Cao
,
X. B.
, and
Shi
,
P.
,
2013
, “
Fuzzy-Model-Based Fault Tolerant Design for Nonlinear Stochastic Systems Against Simultaneous Sensor and Actuator Faults
,”
IEEE Trans. Fuzzy Syst.
,
21
(
5
), pp.
789
799
.
21.
Jia
,
Q. X.
,
Chen
,
W.
, and
Zhang
,
Y. C.
,
2015
, “
Fault Reconstruction and Fault-Tolerant Control Via Learning Observers in Takagi–Sugeno Fuzzy Descriptor Systems With Time Delays
,”
IEEE Trans. Ind. Electron.
,
62
(
6
), pp.
3885
3996
.
22.
Gu
,
Z.
,
Liu
,
J. L.
,
Peng
,
C.
, and
Tian
,
E.
,
2011
, “
Fault-Distribution Dependent Reliable Control for T-S Fuzzy Time-Delayed Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
133
(
6
), p. 064503.
23.
Zhang
,
K.
,
Jiang
,
B.
, and
Shi
,
P.
,
2012
, “
Fault Estimation Observer Design for Discrete-Time Takagi–Sugeno Fuzzy Systems Based on Piecewise Lyapunov Functions
,”
IEEE Trans. Fuzzy Syst.
,
20
(
1
), pp.
192
201
.
24.
Jiang
,
B.
,
Zhang
,
K.
, and
Shi
,
P.
,
2011
, “
Integrated Fault Estimation and Accommodation Design for Discrete-Time Takagi–Sugeno Fuzzy Systems With Actuator Faults
,”
IEEE Trans. Fuzzy Syst.
,
19
(
2
), pp.
291
304
.
25.
Jiang
,
B.
,
Staroswiecki
,
M.
, and
Cocquempot
,
V.
,
2004
, “
Fault Estimation in Nonlinear Uncertain Systems Using Robust/Sliding-Mode Observers
,”
IEE Proc.-Control Theory Appl.
,
151
(
1
), pp.
29
37
.
26.
Zhang
,
X. D.
,
Polycarpou
,
M. M.
, and
Parisini
,
T.
,
2010
, “
Fault Diagnosis of a Class of Nonlinear Uncertain Systems With Lipschitz Nonlinearities Using Adaptive Estimation
,”
Automatica
,
46
(
2
), pp.
290
299
.
27.
Zhang
,
X. D.
,
Parisini
,
T.
, and
Polycarpou
,
M. M.
,
2004
, “
Adaptive Fault-Tolerant Control of Nonlinear Uncertain Systems: An Information-Based Diagnostic Approach
,”
IEEE Trans. Autom. Control
,
49
(
8
), pp.
1259
1274
.
28.
Zhang
,
X. D.
,
2011
, “
Sensor Bias Fault Detection and Isolation in a Class of Nonlinear Uncertain Systems Using Adaptive Estimation
,”
IEEE Trans. Autom. Control
,
56
(
5
), pp.
1220
1226
.
29.
Jiang
,
B.
,
Staroswiecki
,
M.
, and
Cocquempot
,
V.
,
2006
, “
Fault Accommodation for Nonlinear Dynamic Systems
,”
IEEE Trans. Autom. Control
,
51
(
9
), pp.
1578
1583
.
30.
Yan
,
X. G.
,
Spurgeon
,
S. K.
, and
Edwards
,
C.
,
2013
, “
State and Parameter Estimation for Nonlinear Delay Systems Using Sliding Mode Techniques
,”
IEEE Trans. Autom. Control
,
58
(
4
), pp.
1023
1029
.
31.
Han
,
C. S.
,
Zhang
,
G. J.
,
Wu
,
L. G.
, and
Zeng
,
Q. S.
,
2012
, “
Sliding Mode Control of T–S Fuzzy Descriptor Systems With Time-Delay
,”
J. Franklin Inst.
,
349
(
4
), pp.
1430
1444
.
32.
Hamdi
,
H.
,
Rodrigues
,
M.
,
Mechmeche
,
C.
, and
Benhadjbraiek
,
N.
,
2013
, “
Observer Based Fault Tolerant Control for Takagi–Sugeno Nonlinear Descriptor Systems
,”
International Conference on Control, Engineering and Information Technology
, Sousse, Tunisia, June 20, pp.
52
57
.
33.
Yang
,
C. Y.
, and
Zhang
,
Q. L.
,
2009
, “
Multiobjective Control for TCS Fuzzy Singularly Perturbed Systems
,”
IEEE Trans. Fuzzy Syst.
,
17
(
1
), pp.
104
115
.
34.
Feng
,
Z. G.
, and
Shi
,
P.
,
2017
, “
Sliding Mode Control of Singular Stochastic Markov Jump Systems
,”
IEEE Trans. Autom. Control
,
62
(
8
), pp.
4266
4273
.
35.
Zhu
,
Y.
,
Zhong
,
Z.
,
Basin
,
M. V.
, and
Zhou
,
D.
,
2018
, “
A Descriptor System Approach to Stability and Stabilization of Discrete-Time Switched PWA Systems
,”
IEEE Trans. Autom. Control
,
63
(10), pp. 3456–3463.
36.
Li
,
H.
, and
Wang
,
Y.
,
2017
, “
Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks
,”
SIAM J. Control Optim.
,
55
(
6
), pp.
3437
3457
.
37.
Li
,
Y.
,
Li
,
H.
, and
Sun
,
W.
,
2018
, “
Event-Triggered Control for Robust Set Stabilization of Logical Control Networks
,”
Automatica
,
95
, pp.
556
560
.
38.
Tong
,
M. S.
,
Pan
,
Y. L.
,
Li
,
Z. L.
, and
Lin
,
W. Y.
,
2018
, “
Valid Data Based Normalized Cross-Correlation (VDNCC) for Topography Identification
,”
Neurocomputing
,
308
, pp.
184
193
.
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