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.
Issue Section:
Research Papers
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 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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