This paper focuses on the problem of nonfragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems (DFBS) with time-delay in both states and inputs. Based on the parallel distributed compensation approach, the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations.

References

References
1.
Keel
,
L. H.
, and
Bhattacharryya
,
S. P.
,
1997
, “
Robust, Fragile, or Optimal?
,”
IEEE Trans. Autom. Control
,
42
(
8
), pp.
1098
1105
.10.1109/9.618239
2.
Yang
,
G. H.
,
Wang
,
J. L.
, and
Lin
,
C.
,
2000
, “
H∞ Control for Linear Systems With Additive Controller Gain Variations
,”
Int. J. Control
,
73
(
16
), pp.
1500
1506
.10.1080/00207170050163369
3.
Yang
,
H. G.
, and
Wang
,
J. L.
,
2001
, “
Non-Fragile H∞ Control for Linear Systems With Multiplicative Controller Gain Variations
,”
Automatica
,
37
(
5
), pp.
727
737
.
4.
Zhang
,
B. Y.
,
Zhou
,
S. S.
, and
Li
,
T.
,
2007
, “
A New Approach to Robust and Non-Fragile H∞ Control for Uncertain Fuzzy Systems
,”
Inf. Sci.
,
177
, pp.
5118
5133
.10.1016/j.ins.2007.05.004
5.
Yee
,
J. S.
,
Yang
,
G. H.
, and
Wang
,
J. L.
,
2001
, “
Non-Fragile Guaranteed Cost Control for Discrete-Time Uncertain Linear Systems
,”
Int. J. Syst. Sci.
,
32
(
7
), pp.
845
853
.10.1080/00207720117595
6.
Li
,
L.
,
Liu
,
X. D.
, and
Chai
,
T. Y.
,
2009
, “
New Approach on H∞ Control of T-S Fuzzy Systems With Interval Time-Varying Delay
,”
Fuzzy Sets Syst.
,
160
(
12
), pp.
1669
1688
.10.1016/j.fss.2008.11.021
7.
Li
,
Y. M.
,
Xu
,
S. Y.
,
Zhang
,
B. Y.
, and
Chu
,
Y.
,
2008
, “
Robust Stabilization and H∞ Control for Uncertain Fuzzy Neutral Systems With Mixed Time Delays
,”
Fuzzy Sets Syst.
,
159
(
20
), pp.
2730
2748
.10.1016/j.fss.2008.01.030
8.
Zhang
,
B. Y.
,
Lam
,
J.
,
Xu
,
S. Y.
, and
Shu
,
Z.
,
2009
, “
Robust Stabilization of Uncertain T-S Fuzzy Time-Delay Systems With Exponential Estimates
,”
Fuzzy Stes and Systems
,
160
(
12
), pp.
1720
1737
.10.1016/j.fss.2008.10.015
9.
Zhou
,
S. S.
,
Lam
,
J.
, and
Zh
,
W. X.
,
2007
, “
Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and H-Infinity Performance Conditions
,”
IEEE Trans. Fuzzy Syst.
,
15
(
2
), pp.
188
198
.10.1109/TFUZZ.2006.879996
10.
Elliott
,
D. L.
,
1999
,
Bilinear Systems in Encyclopedia of Electrical Engineering
,
Wiley
,
New York
.
11.
Li
,
T. H. S.
, and
Tsai
,
S. H.
,
2007
, “
T-S Fuzzy Bilinear Model and Fuzzy Controller Design for a Class of Nonlinear Systems
,”
IEEE Trans. Fuzzy Syst.
,
3
(
15
), pp.
494
505
.10.1109/TFUZZ.2006.889964
12.
Tsai
,
S. H.
, and
Li
,
T. H. S.
,
2009
, “
Robust Fuzzy Control of a Class Fuzzy Bilinear Systems With Time-Delay
,”
Chaos, Solitons, Fractals
,
39
(
5
), pp.
2028
2040
.10.1016/j.chaos.2007.06.057
13.
Li
,
T. H. S.
,
Tsai
,
S.-H.
,
Lee
,
J.-Z.
,
Hsiao
,
M.-Y.
, and
Chao
,
C.-H.
,
2008
, “
Robust H∞ Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems
,”
IEEE Trans. Syst., Man, Cybern.
,
38
(
2
), pp.
510
526
.10.1109/TSMCB.2007.914706
14.
Wang
,
R. J.
,
Lin
,
W. W.
, and
Wang
,
W. J.
,
2004
, “
Stabilizability of Linear Quadratic State Feedback for Uncertain Fuzzy Time-Delay Systems
,”
IEEE Trans. Syst., Man, Cybern.
,
34
(
2
), pp.
1288
1292
.10.1109/TSMCB.2003.818437
You do not currently have access to this content.