© The Institution of Engineering and Technology
This study investigates the problem of state feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems (SPSs) with parameter uncertainty. The considered system is approximated by Takagi–Sugeno fuzzy model. Based on a matrix spectral norm approach, new sufficient conditions, which ensure the existence of state feedback controller such that the resulting closed-loop system is asymptotically stable, are given. The gains of controllers are obtained by solving a set of ɛ-independent linear matrix inequalities (LMIs) such that, the ill-conditioned problems caused by ɛ can be easily avoided. In contrast to the existing results, the proposed method can be applied to both certain and uncertain SPSs with greater singular perturbation parameter ɛ. A numerical example is provided to illustrate the reduced conservatism of the authors’ results.
References
-
-
1)
-
H.N. Wu
.
Delay-dependent stability analysis and stabilization for discrete-time fuzzy systems with state delay: a fuzzy Layapunov–Krasovskii functional approach.
IEEE Trans. Syst. Man Cybern. B, Cybern.
,
4 ,
954 -
962
-
2)
-
A. Kruszewki ,
R. Wang ,
T.M. Guerra
.
Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete-time TS fuzzy models: a new approach.
IEEE Trans. Autom. Control
,
2 ,
606 -
611
-
3)
-
J. Yoneyama
.
New robust stability condition and design of robust stabilizing controller for Takagi-Sugeno fuzzy time-delay systems.
IEEE Trans. Fuzzy Syst.
,
5 ,
828 -
839
-
4)
-
C.Y. Yang ,
Q.L. Zhang
.
Multiobjective control for T-S fuzzy singularly perturbed systems.
IEEE Trans. Fuzzy Syst.
,
1 ,
104 -
115
-
5)
-
I. Motte ,
G. Campion
.
A slow manifold approach for the control of mobile robots not satisfying the kinematic constraints.
IEEE Trans. Robot. Autom.
,
6 ,
875 -
880
-
6)
-
P. Mei ,
C. Cai ,
Y. Zou
.
Robust fuzzy control of nonlinear singularly perturbed singularly perturbed systems with parametric uncertainties.
Int. J. Innov. Comput. Inf. Control
,
8 ,
2079 -
2086
-
7)
-
G. Hong ,
J. Dong
.
ℋ∞ filtering for fuzzy singularly perturbed systems.
IEEE Trans. Syst., Man Cybern. Part B
,
5 ,
1371 -
1389
-
8)
-
T. Takagi ,
M. Sugeno
.
Fuzzy identification of systems and its applications to model and control.
IEEE Trans. Syst. Man Cybern.
,
116 -
132
-
9)
-
W.C. Su ,
Z. Gajic ,
X.M. Shen
.
The exact slow-fast decomposition of the algebraic Riccati equation of SPSs.
IEEE Trans. Autom. Control
,
9 ,
1456 -
1459
-
10)
-
F.C. Sun ,
L. Li ,
H.X. Li
.
Neuro-fuzzy dynamic-inversion-based adaptive control for robotic manipulators-discrete time case.
IEEE Trans. Ind. Electron.
,
3 ,
1342 -
1351
-
11)
-
H.P. Liu ,
F.C. Sun ,
Z.Q. Sun
.
Stability analysis and synthesis of fuzzy singularly perturbed systems.
IEEE Trans. Fuzzy Syst.
,
3 ,
273 -
284
-
12)
-
W. Assawinchaichote ,
S.K. Nguang
.
Fuzzy H∞ output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach.
IEEE Trans. Fuzzy Syst.
,
3 ,
361 -
371
-
13)
-
H.O. Wang ,
K. Tanaka ,
M.F. Griffin
.
An approach to fuzzy control of nonlinear systems: stability and the design issues.
IEEE Trans. Fuzzy Syst.
,
1 ,
14 -
23
-
14)
-
J. Dong ,
G.H. Yang
.
Robust H∞ control for standard discrete-time singularly perturbed systems.
Proc. IET Control Theory Appl.
,
4 ,
1141 -
1148
-
15)
-
J.W. Kimball ,
P.K. Krein
.
Singular perturbation theory for DC–DC converters and application to PFC converters.
IEEE Trans. Power Electron.
,
6 ,
2970 -
2981
-
16)
-
Y.Y. Wang ,
S.J. Shi ,
Z.J. Zhang
.
A descriptor-system approach to singular perturbation of linear regulators.
IEEE Trans. Autom. Control
,
4 ,
370 -
373
-
17)
-
Kim, B.S., Kim, Y.J., Lim, M.T.: `LQG control for nonstandard singularly perturbed discrete-time systems', Proc. IEEE Int. Conf. on Decision and Control, 2002, 4, p. 3736–3741.
-
18)
-
K. Kiriakidis
.
Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities.
IEEE Trans. Fuzzy Syst.
,
2 ,
269 -
277
-
19)
-
K.B. Datta ,
A. RaiChaudhuri
.
H2/H∞ of discrete singularly perturbed systems: the state feedback case.
Automatica
,
1791 -
1797
-
20)
-
S.K. Nguang ,
P. Shi
.
Fuzzy output feedback control design for nonlinear systems: an LMI approach.
IEEE Trans. Fuzzy Syst.
,
331 -
340
-
21)
-
S.S. Chen ,
Y.C. Chang ,
S.F. Su
.
Robust static output feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach.
IEEE Trans. Fuzzy Syst.
,
2 ,
263 -
272
-
22)
-
J.X. Dong ,
G.H. Yang
.
H∞ control design for fuzzy discrete-time singularly perturbed systems via slow variables feedback: An LMI-based approach.
Inf. Sci.
,
17 ,
3041 -
3058
-
23)
-
H.P. Liu ,
F.C. Sun ,
Y.N. Hu
.
H∞ control for fuzzy singularly perturbed systems.
Fuzzy Sets Syst.
,
1 ,
272 -
291
-
24)
-
McClamroch, N.H.: `A singular perturbation approach to modeling and control of manipulators constrained by a stiff environment', Proc. IEEE Conf. on Decision and Control, December 1989, 3, p. 2407–2411.
-
25)
-
S. Xu ,
G. Feng
.
New results on H∞ control of discrete-time singularly perturbed systems.
Automatica
,
10 ,
2339 -
2343
-
26)
-
W. Assawinchaichote ,
S.K. Nguang
.
ℋ∞ filtering for fuzzy nonlinear singularly-perturbed systems with pole placement constraints: an LMI approach.
IEEE Trans. Signal Process.
,
1659 -
1667
-
27)
-
G. Feng ,
M. Chen ,
D. Sun
.
Approaches to robust filtering design of discrete time fuzzy dynamic systems.
IEEE Trans. Fuzzy Syst.
,
2 ,
331 -
340
-
28)
-
G.H. Yang ,
J.X. Dong
.
Control synthesis of singularly perturbed fuzzy systems.
IEEE Trans. Fuzzy Syst.
,
3 ,
615 -
629
-
29)
-
Jia, H., Zhang, X.D., Sun, H.X.: `Active control of space flexible-joint/flexible-link manipulator', Proc. IEEE Conf. on Robotics Automation and Mechatronics, 21–24 September 2008, p. 812–818.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2010.0142
Related content
content/journals/10.1049/iet-cta.2010.0142
pub_keyword,iet_inspecKeyword,pub_concept
6
6