This paper considers a design problem of dissipative and observer-based finite-time nonfragile control for a class of uncertain discrete-time system with time-varying delay, nonlinearities, external disturbances, and actuator saturation. In particular, in this work, it is assumed that the nonlinearities satisfy Lipschitz condition for obtaining the required results. By choosing a suitable Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained in terms of linear matrix inequalities, which ensures the finite-time boundedness and dissipativeness of the resulting closed-loop system. Meanwhile, the solvability condition for the observer-based finite-time nonfragile control is also established, in which the control gain can be computed by solving a set of matrix inequalities. Finally, a numerical example based on the electric-hydraulic system is provided to illustrate the applicability of the developed control design technique.

References

References
1.
Lee
,
S. Y.
,
Lee
,
W. I.
, and
Park
,
P.
,
2017
, “
Stability Analysis of Discrete-Time Systems With Time-Varying Delays: Generalized Zero Equalities Approach
,”
Int. J. Robust Nonlinear Control
,
27
(6), pp.
981
999
.
2.
Mao
,
Y.
,
Zhang
,
H.
, and
Zhang
,
Z.
,
2017
, “
Finite-Time Stabilization of Discrete-Time Switched Non-Linear Systems Without Stable Subsystems Via Optimal Switching Signals Design
,”
IEEE Trans. Fuzzy Syst.
,
25
(1), pp.
172
180
.
3.
Zhang
,
J.
,
Shi
,
P.
,
Qui
,
J.
, and
Nguang
,
S. K.
,
2015
, “
A Novel Observer-Based Output Feedback Controller Design for Discrete-Time Fuzzy Systems
,”
IEEE Trans. Fuzzy Syst.
,
23
(1), pp.
223
229
.
4.
Sakthivel
,
R.
,
Karthick
,
S. A.
,
Kaviarasan
,
B.
, and
Lim
,
Y.
,
2017
, “
Reliable State Estimation of Switched Neutral System With Nonlinear Actuator Faults Via Sampled-Data Control
,”
Appl. Math. Comput.
,
311
, pp.
129
147
.
5.
Pan
,
H.
,
Sun
,
W.
,
Gao
,
H.
, and
Jing
,
X.
,
2016
, “
Disturbance Observer-Based Adaptive Tracking Control With Actuator Saturation and Its Application
,”
IEEE Trans. Autom. Sci. Eng.
,
13
(2), pp.
868
875
.
6.
Bibi
,
H.
,
Bedouhene
,
F.
,
Zemouche
,
A.
,
Karimi
,
H. R.
, and
Kheloufi
,
H.
,
2017
, “
Output Feedback Stabilization of Switching Discrete-Time Linear Systems With Parameter Uncertainties
,”
J. Franklin Inst.
,
354
(14), pp.
5895
5918
.
7.
Hui
,
G.
, and
Xie
,
X.
,
2016
, “
Novel Observer-Based Output Feedback Control Synthesis of Discrete-Time Nonlinear Control Systems Via a Fuzzy Approach
,”
Neurocomputing
,
214
, pp.
16
22
.
8.
Mobayen
,
S.
,
2016
, “
Optimal LMI-Based State Feedback Stabilizer for Uncertain Nonlinear Systems With Time-Varying Uncertainties and Disturbances
,”
Complexity
,
21
(
6
), pp.
356
362
.
9.
Lin
,
X.
,
Li
,
X.
,
Li
,
S.
, and
Zou
,
Y.
,
2016
, “
Finite-Time Boundedness of Switched Systems With Sector Bounded Nonlinearity and Constant Time Delay
,”
Appl. Math. Computation
,
274
, pp.
25
40
.
10.
Liu
,
H.
, and
Lin
,
X.
,
2015
, “
Finite-Time H Control for a Class of Nonlinear System With Time-Varying Delay
,”
Neurocomputing
,
149
(pt C), pp.
1481
1489
.
11.
Song
,
J.
, and
He
,
S.
,
2015
, “
Finite-Time Robust Passive Control for a Class of Uncertain Lipschitz Nonlinear Systems With Time-Delays
,”
Neurocomputing
,
159
, pp.
275
281
.
12.
Pan
,
H.
,
Sun
,
W.
,
Gao
,
H.
, and
Yu
,
J.
,
2015
, “
Finite-Time Stabilization for Vehicle Active Suspension Systems With Hard Constraints
,”
IEEE Trans. Intell. Transp. Syst.
,
16
(
5
), pp.
2663
2672
.
13.
Liu
,
H.
,
Shi
,
P.
,
Karimi
,
H. R.
, and
Chadli
,
M.
,
2016
, “
Finite-Time Stability and Stabilization for a Class of Nonlinear Systems With Time-Varying Delay
,”
Int. J. Syst. Sci.
,
47
(
6
), pp.
1433
1444
.
14.
Liu
,
D.
, and
Yang
,
G. H.
,
2018
, “
Event-Triggered Non-Fragile Control for Linear Systems With Actuator Saturation and Disturbances
,”
Inf. Sci.
,
429
, pp.
1
11
.
15.
Zhang
,
Z.
,
Zhang
,
H.
,
Wang
,
Z.
, and
Shan
,
Q.
,
2017
, “
Non-Fragile Exponential H∞ Control for a Class of Non-Linear Networked Control Systems With Short Time-Varying Delay Via Output Feedback Controller
,”
IEEE Trans. Cybern.
,
47
(8), pp.
2008
2019
.
16.
Willems
,
J. C.
,
1972
, “
Dissipative Dynamical Systems—Part I: General Theory
,”
Arch. Ration. Mech. Anal.
,
45
(
5
), pp.
321
351
.
17.
Shi
,
P.
,
Su
,
X.
, and
Li
,
F.
,
2016
, “
Dissipativity Based Filtering for Fuzzy Switched Systems With Stochastic Perturbations
,”
IEEE Trans. Autom. Control
,
61
(
6
), pp.
1694
1699
.
18.
Ma
,
Y. C.
,
Chen
,
M. H.
, and
Zhang
,
Q. L.
,
2015
, “
Memory Dissipative Control for Singular T-S Fuzzy Time-Varying Delay Systems Under Actuator Saturation
,”
J. Franklin Inst.
,
352
(
10
), pp.
3947
3970
.
19.
Ma
,
Y.
, and
Chen
,
M.
,
2016
, “
Finite-Time Non-Fragile Dissipative Control for Uncertain TS Fuzzy System With Time-Varying Delay
,”
Neurocomputing
,
177
, pp.
509
514
.
20.
Wu
,
Z. G.
,
Shi
,
P.
,
Su
,
H.
, and
Lu
,
R.
,
2015
, “
Dissipativity Based Sampled Data Fuzzy Control Design and Its Application to Truck-Trailer System
,”
IEEE Trans. Fuzzy Syst.
,
23
(
5
), pp.
1669
1679
.
21.
Li
,
S.
, and
Ma
,
Y.
,
2018
, “
Finite-Time Dissipative Control for Singular Markovian Jump Systems Via Quantizing Approach
,”
Nonlinear Anal.: Hybrid Syst.
,
27
, pp.
323
340
.
22.
Xia
,
W.
,
Li
,
Y.
,
Chu
,
Y.
,
Xu
,
S.
, and
Zhang
,
Z.
,
2017
, “
Dissipative Filter Design for Uncertain Markovian Jump System With Mixed Delays and Unknown Transition Rates
,”
Signal Process.
,
141
, pp.
176
186
.
23.
Sakthivel
,
R.
,
Rathika
,
M.
,
Santra
,
S.
, and
Muslim
,
M.
,
2017
, “
Observer-Based Dissipative Control for Markovian Jump Systems Via Delta Operators
,”
Int. J. Syst. Sci.
,
48
(
2
), pp.
247
256
.
24.
Ma
,
Y.
,
Jia
,
X.
, and
Liu
,
D.
,
2016
, “
Robust Finite-Time H∞ Control for Discrete-Time Singular Markovian Jump Systems With Time-Varying Delay and Actuator Saturation
,”
Appl. Math. Comput.
,
286
, pp.
213
227
.
25.
Yang
,
W.
, and
Tong
,
S.
,
2015
, “
Output Feedback Stabilization of Switched Fuzzy Systems With Time-Delay and Actuator Saturation
,”
Neurocomputing
,
164
, pp.
173
181
.
26.
Ma
,
Y.
,
Yang
,
P.
,
Yan
,
Y.
, and
Zhang
,
Q.
,
2017
, “
Robust Observer-Based Passive Control for Uncertain Singular Time-Delay Systems With Actuator Saturation
,”
ISA Trans.
,
67
, pp.
9
18
.
27.
Wei
,
Y.
,
Zheng
,
W. X.
, and
Xu
,
S.
,
2015
, “
Robust Output Feedback Control of Uncertain Time-Delay Systems With Actuator Saturation and Disturbances
,”
J. Franklin Inst.
,
352
(
5
), pp.
2229
2248
.
28.
Wang
,
X.
,
Zuo
,
X.
,
Liu
,
J.
, and
Liang
,
H.
,
2017
, “
Robust Observer-Based H∞ Control for Uncertain Discrete Time-Delay Systems With Nonlinearities Eletric-Hydraulic System Under Hölder Condition
,”
Optim. Control Appl. Methods
,
38
(
6
), pp.
1120
1131
.
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