This paper is concerned with the design of reliable robust H fuzzy control for uncertain nonlinear continuous-time systems with Markovian jumping actuator faults. The Takagi and Sugeno fuzzy model is employed to represent an uncertain nonlinear system with Markovian jumping actuator faults. First, based on the parallel distributed compensation (PDC) scheme, a sufficient condition such that the closed-loop fuzzy system is robustly stochastically stable and satisfies a prescribed level of H-disturbance attenuation is derived. In the derivation process, a stochastic Lyapunov function is used to test the stability and H performance of the system. Then, a new improved linear matrix inequality (LMI) formulation is applied to this condition to alleviate the interrelation between the stochastic Lyapunov matrix and system matrices containing controller variables, which results in a tractable LMI-based condition for the existence of reliable and robust H fuzzy controllers. A suboptimal fuzzy controller is proposed to minimize the level of disturbance attenuation subject to the LMI constraints. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

1.
Takagi
,
T.
, and
Sugeno
,
M.
, 1985, “
Fuzzy Identification of Systems and Its Applications to Modeling and Control
,”
IEEE Trans. Syst. Man Cybern.
0018-9472,
15
, pp.
116
132
.
2.
Wang
,
H. O.
,
Tanaka
,
K.
, and
Griffin
,
M. F.
, 1996, “
An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
4
(
1
), pp.
14
23
.
3.
Cao
,
S. G.
,
Rees
,
N. W.
, and
Feng
,
G.
, 1996, “
H-Infinity Control of Nonlinear Continuous-Time Systems Based on Dynamical Fuzzy Models
,”
Int. J. Syst. Sci.
0020-7721,
27
, pp.
821
830
.
4.
Tanaka
,
K.
, and
Wang
,
H. O.
, 2001,
Fuzzy Control Systems Design and Analysis, A Linear Matrix Inequality Approach
,
Wiley
,
New York
.
5.
Tuan
,
H. D.
,
Apkarian
,
P.
,
Narikiyo
,
T.
, and
Yamamoto
,
Y.
, 2001, “
Parameterized Linear Matrix Inequality Techniques in Fuzzy Control System Design
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
9
(
2
), pp.
324
332
.
6.
Nguang
,
S. K.
, and
Shi
,
P.
, 2003, “
H∞ Fuzzy Output Feedback Control Design for Nonlinear Systems: an LMI Approach
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
11
(
3
), pp.
331
340
.
7.
Teixeira
,
M. C. M.
,
Assunção
,
E.
, and
Avellar
,
R. G.
, 2003, “
On Relaxed LMI-Based Designs for Fuzzy Regulators and Fuzzy Observers
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
11
(
5
), pp.
613
623
.
8.
Tanaka
,
K.
,
Ikeda
,
T.
, and
Wang
,
H. O.
, 1996, “
Robust Stabilization of a Class of Uncertain Nonlinear Systems Via Fuzzy Control: Quadratic Stabilizability, H∞ Control Theory, and Linear Matrix Inequalities
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
4
(
1
), pp.
1
13
.
9.
Lee
,
H. J.
,
Park
,
J. B.
, and
Chen
,
G.
, 2001, “
Robust Fuzzy Control of Nonlinear Systems With Parametric Uncertainties
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
9
(
2
), pp.
369
379
.
10.
Lee
,
K. R.
,
Jeung
,
E. T.
, and
Park
,
H. B.
, 2001, “
Robust Fuzzy H∞ Control for Uncertain Nonlinear Systems Via State Feedback: an LMI Approach
,”
Fuzzy Sets Syst.
0165-0114,
120
, pp.
123
134
.
11.
Wu
,
H.-N.
, and
Cai
,
K.-Y.
, 2004, “
H2 Guaranteed Cost Fuzzy Control for Uncertain Nonlinear Systems Via Linear Matrix Inequalities
,”
Fuzzy Sets Syst.
0165-0114,
148
, pp.
411
429
.
12.
Vidyasagar
,
M.
, and
Viswanadham
,
N.
, 1985, “
Reliable Stabilization Using a Multicontroller Configuration
,”
Automatica
0005-1098,
21
, pp.
599
602
.
13.
Stoustrup
,
J.
, and
Blondel
,
V. D.
, 2004, “
Fault Tolerant Control: a Simultaneous Stabilization Result
,”
IEEE Trans. Autom. Control
0018-9286,
49
(
2
), pp.
305
310
.
14.
Veillette
,
R. J.
,
Medanic
,
J. V.
, and
Perkins
,
W. R.
, 1992, “
Design of Reliable Control Systems
,”
IEEE Trans. Autom. Control
0018-9286,
37
(
3
), pp.
290
304
.
15.
Veillette
,
R. J.
, 1995, “
Reliable Linear-Quadratic State-Feedback Control
,”
Automatica
0005-1098,
31
(
1
), pp.
137
143
.
16.
Seo
,
C.-J.
, and
Kim
,
B. K.
, 1996, “
Robust and Reliable H∞ Control for Linear Systems With Parameter Uncertainty and Actuator Failure
,”
Automatica
0005-1098,
32
(
3
), pp.
465
467
.
17.
Yang
,
G.-H.
,
Wang
,
J. L.
, and
Soh
,
Y. C.
, 2001, “
Reliable H∞ Controller Design for Linear Systems
,”
Automatica
0005-1098,
37
(
5
), pp.
717
725
.
18.
Zhao
,
Q.
, and
Jiang
,
J.
, 1998, “
Reliable State Feedback Control System Design Against Actuator Failures
,”
Automatica
0005-1098,
34
(
10
), pp.
1267
1272
.
19.
Lam
,
J.
, and
Cao
,
Y. Y.
, 1999, “
Simultaneous Linear-Quadratic Optimal Control Design Via Static Output Feedback
,”
Int. J. Robust Nonlinear Control
1049-8923,
9
, pp.
551
558
.
20.
Liao
,
F.
,
Wang
,
J. L.
, and
Yang
,
G.-H.
, 2002, “
Reliable Robust Flight Tracking Control: an LMI Approach
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
10
(
1
), pp.
76
89
.
21.
Yang
,
G.-H.
,
Lam
,
J.
, and
Wang
,
J. L.
, 1998, “
Reliable H∞ Control for Affine Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
43
(
8
), pp.
1112
1117
.
22.
Liang
,
Y.-W.
,
Liaw
,
D.-C.
, and
Lee
,
T.-C.
, 2000, “
Reliable Control of Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
4
), pp.
706
710
.
23.
Yang
,
G.-H.
,
Wang
,
J. L.
, and
Soh
,
Y. C.
, 2000, “
Reliable Guaranteed Cost Control for Uncertain Nonlinear Systems
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
11
), pp.
2188
2192
.
24.
Wu
,
H.-N.
, 2004, “
Reliable LQ Fuzzy Control for Nonlinear Discrete-Time Systems Via LMIs
,”
IEEE Trans. Syst. Sci. Cybern.
0536-1567,
34
(
2
), pp.
1270
1275
.
25.
Wu
,
H.-N.
, 2004, “
Reliable LQ Fuzzy Control for Continuous-Time Nonlinear Systems With Actuator Faults
,”
IEEE Trans. Syst. Sci. Cybern.
0536-1567,
34
(
4
), pp.
1743
1752
.
26.
Boyd
,
S.
,
Ghaoui
,
L. E.
,
Feron
,
E.
, and
Balakrishnan
,
V.
, 1994,
Linear Matrix Inequalities in System and Control Theory
,
SIAM
,
Philadelphia, PA
.
27.
Gahinet
,
P.
,
Nemirovski
,
A.
,
Laub
,
A. J.
, and
Chilali
,
M.
, 1995,
LMI Control Toolbox
,
Math Works Inc.
,
Natick, MA
.
28.
Mahmoud
,
M. M.
,
Jiang
,
J.
, and
Zhang
,
Y.
, 2003,
Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis
,
Springer-Verlag
,
Berlin, Heidelberg
.
29.
Taylor
,
H. M.
, and
Karlin
,
S.
, 1984,
An Introduction to Stochastic Modelling
,
Academic
,
Orlando, FL
.
30.
Shi
,
P.
, and
Boukas
,
E. K.
, 1997, “
H∞-Control for Markovian Jumping Linear Systems With Parametric Uncertainty
,”
J. Optim. Theory Appl.
0022-3239,
95
(
1
), pp.
75
99
.
31.
Cao
,
Y.-Y.
, and
Lam
,
J.
, 2000, “
Robust H∞ Control of Uncertain Markovian Jump Systems With Time-Delay
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
1
), pp.
77
83
.
32.
Petersen
,
I. R.
, 1987, “
A Stabilization Algorithm for a Class of Uncertain Linear Systems
,”
Syst. Control Lett.
0167-6911,
8
, pp.
351
357
.
33.
Kushner
,
H. J.
, 1967,
Stochastic Stability and Control
,
Academic
,
New York
.
34.
Vidyasagar
,
M.
, 1993,
Nonlinear Systems Analysis
,
2nd ed.
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
You do not currently have access to this content.