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The authors consider in this study the problem of reducing conservatism in stability and stabilisation margin of continuous-time Takagi–Sugeno (T–S) fuzzy systems, where the fuzzy weighting functions are assumed to be differentiable and their ranges of variation are assumed to be bounded by some parameters. To compensate for the latter constraint, the conventional quadratic relaxation technique is appropriately modified and the free weighting matrix for the former assumption is further indexed in accordance with the fuzzy weighting functions to derive more degrees of freedom. By applying the relaxed free weighting matrices into the resulting quadratic summation representation and by utilising the linearity of the constraints on the time-derivative of the membership functions, better performance behaviour can be achieved over existing works, which is demonstrated theoretically and by some examples.
References
-
-
1)
-
A. Sala ,
C. Ariño
.
Relaxed stability and performance LMI conditions for Takagi–Sugeno fuzzy systems with polynomial constraints on membership function shapes.
IEEE Trans. Fuzzy Syst.
,
5 ,
1328 -
1336
-
2)
-
C. Lin ,
Q.G. Wang ,
T.H. Lee ,
Y. He
.
Stability conditions for time-delay fuzzy systems using fuzzy weighting-dependent approach.
IET Control Theory Appl.
,
1 ,
127 -
132
-
3)
-
L.A. Mozelli ,
R.M. Palhares ,
F.O. Souza ,
E.M.A.M. Mendes
.
Reducing conservativeness in recent stability conditions of TS fuzzy systems.
Automatica
,
6 ,
1580 -
1583
-
4)
-
H.K. Lam ,
S.C. Tan
.
Stability analysis of fuzzy-model-based control systems: application on regulation of switching DC–DC converter.
IET Control Theory Appl.
,
8 ,
1093 -
1106
-
5)
-
M.C.M. Teixeira ,
E. Assunção ,
R.G. Avellar
.
On relaxed LMI-based designs for fuzzy regulators and fuzzy observers.
IEEE Trans. Fuzzy Syst.
,
5 ,
613 -
623
-
6)
-
F. Delmotte ,
T.M. Guerra ,
M. Ksantini
.
Continuous Takagi–Sugeno's models: reduction of the number of LMI conditions in various fuzzy control design technics.
IEEE Trans. Fuzzy Syst.
,
3 ,
426 -
438
-
7)
-
V.F. Montagner ,
R.C.L.F. Oliveira ,
P.L.D. Peres
.
Convergent LMI relaxations for quadratic stabilizability and ℋ∞ control of Takagi–Sugeno fuzzy systems.
IEEE Trans. Fuzzy Syst.
,
4 ,
863 -
873
-
8)
-
T. Takagi ,
M. Sugeno
.
Fuzzy identification of systems and its application to modeling and control.
IEEE Trans. Syst. Man Cybern.
,
1 ,
116 -
132
-
9)
-
K. Tanaka ,
T. Hori ,
H.O. Wang
.
A multiple Lyapunov function approach to stabilization of fuzzy control systems.
IEEE Trans. Fuzzy Syst.
,
4 ,
582 -
589
-
10)
-
C. Ariño ,
A. Sala
.
Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure.
Eng. Appl. Artif. Intell.
,
8 ,
1036 -
1046
-
11)
-
B.-J. Rhee ,
S. Won
.
A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design.
Fuzzy Set. Syst.
,
9 ,
1211 -
1228
-
12)
-
H.K. Lam
.
Sampled-data fuzzy-model-based control systems: stability analysis with consideration of analogue-to-digital converter and digital-to-analogue converter.
IET Control Theory Appl.
,
7 ,
1131 -
1144
-
13)
-
X. Liu ,
Q. Zhang
.
New approaches to ℋ∞ controller designs based on fuzzy observers for T–S fuzzy systems via LMI.
Automatica
,
9 ,
1571 -
1582
-
14)
-
S. Lee
.
(2000)
Design of computers and other complex digital devices.
-
15)
-
E. Kim ,
H. Lee
.
New approaches to relaxed quadratic stability condition of fuzzy control systems.
IEEE Trans. Fuzzy Syst.
,
5 ,
523 -
534
-
16)
-
A. Sala
.
On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems.
Annu. Rev. Control
,
48 -
58
-
17)
-
A. Sala ,
C. Ariño
.
Relaxed stability and performance conditions for Takagi–Sugeno fuzzy systems with knowledge on membership function overlap.
IEEE Trans. Syst. Man Cybern B, Cybern.
,
3 ,
727 -
732
-
18)
-
C.-H. Fang ,
Y.-S. Liu ,
S.-W. Kau ,
L. Hong ,
C.-H. Lee
.
A new LMI-based approach to relaxed quadratic stabilisation of T–S fuzzy control systems.
IEEE Trans. Fuzzy Syst.
,
3 ,
386 -
397
-
19)
-
X. Liu ,
Q. Zhang
.
New approaches to ℋ∞ controller designs based on fuzzy observers for T–S fuzzy systems via LMI.
Automatica
,
5 ,
1571 -
1582
-
20)
-
H.K. Lam
.
Stability analysis of T–S fuzzy control systems using parameter-dependent Lyapunov function.
IET Control Theory Appl.
,
6 ,
750 -
762
-
21)
-
S. Boyd ,
L.E. Ghaoui ,
E. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequalities in system and control theory.
-
22)
-
A. Sala ,
C. Arino
.
Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya's theorem.
Fuzzy Set. Syst.
,
24 ,
2671 -
2686
-
23)
-
K. Tanaka ,
H.O. Wang
.
(2001)
Fuzzy control systems design and analysis: a linear matrix inequality approach.
-
24)
-
L.A. Mozelli ,
R.M. Palhares ,
G.S. Avellar
.
A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems.
Inf. Sci.
,
8 ,
1149 -
1162
-
25)
-
Jadbabaie, A.: `A reduction in conservatism in stability and ℒ', IFAC World Congress, 1999, Beijing, China.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2011.0009
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