This paper considers a global sliding mode control (GSMC) approach for the stabilization of uncertain chaotic systems with multiple delays and input nonlinearities. By designing the global sliding mode surface, the offered scheme eliminates reaching phase problem. The offered control law is formulated based on state estimation, Lyapunov–Krasovskii stability theory, and linear matrix inequality (LMI) technique which present the asymptotic stability conditions. Moreover, the proposed design approach guarantees the robustness against multiple delays, nonlinear inputs, nonlinear functions, external disturbances, and parametric uncertainties. Simulation results for the presented controller demonstrate the efficiency and feasibility of the suggested procedure.

References

References
1.
Li
,
Y.
, and
Hou
,
Z.
,
2014
, “
Data-Driven Asymptotic Stabilization for Discrete-Time Nonlinear Systems
,”
Syst. Control Lett.
,
64
, pp.
79
85
.
2.
Zhong
,
H.
,
Wang
,
Q.
,
Yu
,
J.-H.
,
Wei
,
Y.-H.
, and
Wang
,
Y.
,
2016
, “
Discrete Sliding Mode Adaptive Vibration Control for Space Frame Based on Characteristic Model
,”
ASME J. Comput. Nonlinear Dyn.
,
12
(
1
), p.
011003
.
3.
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
.
4.
Mobayen
,
S.
,
2015
, “
An Adaptive Chattering-Free PID Sliding Mode Control Based on Dynamic Sliding Manifolds for a Class of Uncertain Nonlinear Systems
,”
Nonlinear Dyn.
,
82
(
1–2
), pp.
53
60
.
5.
Mobayen
,
S.
, and
Baleanu
,
D.
,
2017
, “
Linear Matrix Inequalities Design Approach for Robust Stabilization of Uncertain Nonlinear Systems With Perturbation Based on Optimally-Tuned Global Sliding Mode Control
,”
J. Vib. Control
,
23
(
8
), pp.
1285
1295
.
6.
Hajmohammadi
,
R.
,
NasiriSoloklo
,
H.
, and
Farsangi
,
M.
,
2013
, “
The Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems With Constraint
,”
J. Electr. Comput. Eng. Innovations
,
1
(
1
), pp.
51
55
.http://jecei.srttu.edu/article_21_5.html
7.
Hajmohammadi
,
R.
,
Vali
,
M. A.
, and
Samavat
,
M.
,
2014
, “
Optimal Control of Nonlinear Systems Using the Shifted Legendre Polynomials
,”
Majlesi J. Electr. Eng.
,
8
(
2
), pp.
33
37
.http://mjee.iaumajlesi.ac.ir/index/index.php/ee/article/view/1167
8.
Kiamini
,
S.
,
Jalilvand
,
A.
, and
Mobayen
,
S.
,
2016
, “
Control of Tension Leg Platforms With Multiple Time-Varying Delays in Offshore Floating Wind Turbines Based on LMI Method
,”
Tabriz J. Electr. Eng.
,
46
(
3
), pp.
277
285
.http://tjee.tabrizu.ac.ir/article_5148_c27f66f90d5232e11030e0422bfb6114.pdf
9.
Mobayen
,
S.
, and
Majd
,
V. J.
,
2012
, “
Robust Tracking Control Method Based on Composite Nonlinear Feedback Technique for Linear Systems With Time-Varying Uncertain Parameters and Disturbances
,”
Nonlinear Dyn.
,
70
(
1
), pp.
171
180
.
10.
Mobayen
,
S.
,
2014
, “
Design of CNF-Based Nonlinear Integral Sliding Surface for Matched Uncertain Linear Systems With Multiple State-Delays
,”
Nonlinear Dyn.
,
77
(
3
), pp.
1047
1054
.
11.
Mobayen
,
S.
,
2014
, “
Robust Tracking Controller for Multivariable Delayed Systems With Input Saturation Via Composite Nonlinear Feedback
,”
Nonlinear Dyn.
,
76
(
1
), pp.
827
838
.
12.
Mobayen
,
S.
,
Tchier
,
F.
, and
Ragoub
,
L.
,
2017
, “
Design of an Adaptive Tracker for n-Link Rigid Robotic Manipulators Based on Super-Twisting Global Nonlinear Sliding Mode Control
,”
Int. J. Syst. Sci.
,
48
(
9
), pp.
1990
2002
.
13.
Mobayen
,
S.
,
2015
, “
An LMI-Based Robust Tracker for Uncertain Linear Systems With Multiple Time-Varying Delays Using Optimal Composite Nonlinear Feedback Technique
,”
Nonlinear Dyn.
,
80
(
1–2
), pp.
917
927
.
14.
Mobayen
,
S.
,
2015
, “
An LMI-Based Robust Controller Design Using Global Nonlinear Sliding Surfaces and Application to Chaotic Systems
,”
Nonlinear Dyn.
,
79
(
2
), pp.
1075
1084
.
15.
Mobayen
,
S.
,
Majd
,
V. J.
, and
Sojoodi
,
M.
,
2012
, “
An LMI-Based Composite Nonlinear Feedback Terminal Sliding-Mode Controller Design for Disturbed MIMO Systems
,”
Math. Comput. Simul.
,
85
, pp.
1
10
.
16.
Mobayen
,
S.
, and
Tchier
,
F.
,
2015
, “
A New LMI-Based Robust Finite-Time Sliding Mode Control Strategy for a Class of Uncertain Nonlinear Systems
,”
Kybernetika
,
51
(
6
), pp.
1035
1048
.https://dml.cz/handle/10338.dmlcz/144823
17.
Mobayen
,
S.
,
Majd
,
V. J.
, and
Sojoodi
,
M.
,
2012
, “
An LMI-Based Finite-Time Tracker Design Using Nonlinear Sliding Surfaces
,”
20th Iranian Conference on Electrical Engineering
(
ICEE
), Tehran, Iran, May 15–17, pp.
810
815
.
18.
Mobayen
,
S.
, and
Tchier
,
F.
,
2017
, “
Synchronization of a Class of Uncertain Chaotic Systems With Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach
,”
Asian J. Control
, epub.
19.
Mobayen
,
S.
,
Volos
,
C. K.
,
Kaçar
,
S.
, and
Çavuşoğlu
,
Ü.
,
2017
, “
New Class of Chaotic Systems With Equilibrium Points like a Three-Leaved Clover
,”
Nonlinear Dyn.
, epub.
20.
Boulkroune
,
A.
,
Bouzeriba
,
A.
,
Hamel
,
S.
, and
Bouden
,
T.
,
2014
, “
A Projective Synchronization Scheme Based on Fuzzy Adaptive Control for Unknown Multivariable Chaotic Systems
,”
Nonlinear Dyn.
,
78
(
1
), pp.
433
447
.
21.
Hung
,
J. Y.
,
Gao
,
W.
, and
Hung
,
J. C.
,
1993
, “
Variable Structure Control: A Survey
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
2
22
.
22.
Mobayen
,
S.
, and
Tchier
,
F.
,
2016
, “
Design of an Adaptive Chattering Avoidance Global Sliding Mode Tracker for Uncertain Non-Linear Time-Varying Systems
,”
Trans. Inst. Meas. Control
,
39
(
10
), pp.
1547
1558
.
23.
Mobayen
,
S.
,
2015
, “
Fast Terminal Sliding Mode Controller Design for Nonlinear Second‐Order Systems With Time‐Varying Uncertainties
,”
Complexity
,
21
(
2
), pp.
239
244
.
24.
Majd
,
V. J.
, and
Mobayen
,
S.
,
2015
, “
An ISM-Based CNF Tracking Controller Design for Uncertain MIMO Linear Systems With Multiple Time-Delays and External Disturbances
,”
Nonlinear Dyn.
,
80
(
1–2
), pp.
591
613
.
25.
Mobayen
,
S.
,
2015
, “
Fast Terminal Sliding Mode Tracking of Non-Holonomic Systems With Exponential Decay Rate
,”
IET Control Theory Appl.
,
9
(
8
), pp.
1294
1301
.
26.
Mobayen
,
S.
,
2015
, “
Finite-Time Tracking Control of Chained-Form Nonholonomic Systems With External Disturbances Based on Recursive Terminal Sliding Mode Method
,”
Nonlinear Dyn.
,
80
(
1–2
), pp.
669
683
.
27.
Mobayen
,
S.
, and
Javadi
,
S.
,
2017
, “
Disturbance Observer and Finite-Time Tracker Design of Disturbed Third-Order Nonholonomic Systems Using Terminal Sliding Mode
,”
J. Vib. Control
,
23
(
2
), pp.
181
189
.
28.
Mobayen
,
S.
,
Yazdanpanah
,
M. J.
, and
Majd
,
V. J.
,
2011
, “
A Finite-Time Tracker for Nonholonomic Systems Using Recursive Singularity-Free FTSM
,”
American Control Conference
(
ACC
), San Francisco, CA, June 29–July 1, pp.
1720
1725
.
29.
Mobayen
,
S.
,
Majd
,
V. J.
, and
Asemani
,
M. H.
,
2011
, “
Selection of Nonlinear Function in Integral Sliding Mode-Based Composite Nonlinear Feedback Method for Transient Improvement of Uncertain Linear Systems
,”
Second International Conference on Control, Instrumentation and Automation
(
ICCIA
), Shiraz, Iran, Dec. 27–29, pp.
513
518
.
30.
Mobayen
,
S.
, and
Tchier
,
F.
,
2017
, “
A Novel Robust Adaptive Second-Order Sliding Mode Tracking Control Technique for Uncertain Dynamical Systems With Matched and Unmatched Disturbances
,”
Int. J. Control, Autom. Syst.
,
15
(
3
), pp.
1097
1106
.
31.
Mobayen
,
S.
, and
Tchier
,
F.
,
2017
, “
Nonsingular Fast Terminal Sliding Mode Stabilizer for a Class of Uncertain Nonlinear Systems Based on Disturbance Observer
,”
Scientia Iranica
,
24
(
3
), pp.
1410
1418
.
32.
Choi
,
H.-S.
,
Park
,
Y.-H.
,
Cho
,
Y.
, and
Lee
,
M.
,
2001
, “
Global Sliding-Mode Control. Improved Design for a Brushless DC Motor
,”
IEEE Control Syst.
,
21
(
3
), pp.
27
35
.
33.
Mobayen
,
S.
, and
Baleanu
,
D.
,
2016
, “
Stability Analysis and Controller Design for the Performance Improvement of Disturbed Nonlinear Systems Using Adaptive Global Sliding Mode Control Approach
,”
Nonlinear Dyn.
,
83
(
3
), pp.
1557
1565
.
34.
Mobayen
,
S.
,
2015
, “
A Novel Global Sliding Mode Control Based on Exponential Reaching Law for a Class of Underactuated Systems With External Disturbances
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
2
), p.
021011
.
35.
Xi
,
X.
,
Mobayen
,
S.
,
Ren
,
H.
, and
Jafari
,
S.
,
2017
, “
Robust Finite-Time Synchronization of a Class of Chaotic Systems Via Adaptive Global Sliding Mode Control
,”
J. Vib. Control
, epub.
36.
Mobayen
,
S.
,
2015
, “
An Adaptive Fast Terminal Sliding Mode Control Combined With Global Sliding Mode Scheme for Tracking Control of Uncertain Nonlinear Third-Order Systems
,”
Nonlinear Dyn.
,
82
(
1–2
), pp.
599
610
.
37.
Mobayen
,
S.
, and
Tchier
,
F.
,
2017
, “
Robust Global Second-Order Sliding Mode Control With Adaptive Parameter-Tuning Law for Perturbed Dynamical Systems
,”
Trans. Inst. Meas. Control
, epub.
38.
Vaseghi
,
B.
,
Pourmina
,
M. A.
, and
Mobayen
,
S.
,
2017
, “
Finite-Time Chaos Synchronization and Its Application in Wireless Sensor Networks
,”
Trans. Inst. Meas. Control
, epub.
39.
Mofid
,
O.
, and
Mobayen
,
S.
,
2017
, “
Adaptive Synchronization of Fractional-Order Quadratic Chaotic Flows With Nonhyperbolic Equilibrium
,”
J. Vib. Control
, epub.
40.
Xiu
,
C.
,
Hou
,
J.
,
Xu
,
G.
, and
Zang
,
Y.
,
2017
, “
Improved Fast Global Sliding Mode Control Based on the Exponential Reaching Law
,”
Adv. Mech. Eng.
,
9
(
2
), pp. 1–8.
41.
Chu
,
Y.
,
Fang
,
Y.
, and
Fei
,
J.
,
2017
, “
Adaptive Neural Dynamic Global PID Sliding Mode Control for MEMS Gyroscope
,”
Int. J. Mach. Learn. Cybern.
,
8
(
5
), pp.
1707
1718
.
42.
Liu
,
L.
,
Han
,
Z.
, and
Li
,
W.
,
2009
, “
Global Sliding Mode Control and Application in Chaotic Systems
,”
Nonlinear Dyn.
,
56
(
1
), pp.
193
198
.
43.
Golestani
,
M.
,
Mobayen
,
S.
, and
Tchier
,
F.
,
2016
, “
Adaptive Finite-Time Tracking Control of Uncertain Non-Linear n-Order Systems With Unmatched Uncertainties
,”
IET Control Theory Appl.
,
10
(
14
), pp.
1675
1683
.
44.
Oliveira
,
T. R.
,
Estrada
,
A.
, and
Fridman
,
L. M.
,
2017
, “
Global and Exact HOSM Differentiator With Dynamic Gains for Output-Feedback Sliding Mode Control
,”
Automatica
,
81
, pp.
156
163
.
45.
Nik
,
H. S.
, and
Golchaman
,
M.
,
2014
, “
Chaos Control of a Bounded 4D Chaotic System
,”
Neural Comput. Appl.
,
25
(
3–4
), pp.
683
692
.
46.
Just
,
L. W.
,
DeLuca
,
A. M.
, and
Palazotto
,
A. N.
,
2016
, “
Nonlinear Dynamic Analysis of an Icosahedron Frame Which Exhibits Chaotic Behavior
,”
ASME J. Comput. Nonlinear Dyn.
,
12
(
1
), p.
011006
.
47.
Singh
,
A. K.
,
Yadav
,
V. K.
, and
Das
,
S.
,
2016
, “
Dual Combination Synchronization of the Fractional Order Complex Chaotic Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
12
(
1
), p.
011017
.
48.
Vaseghi
,
B.
,
Pourmina
,
M. A.
, and
Mobayen
,
S.
,
2017
, “
Secure Communication in Wireless Sensor Networks Based on Chaos Synchronization Using Adaptive Sliding Mode Control
,”
Nonlinear Dyn.
,
89
(
3
), pp.
1689
1704
.
49.
Boedecker
,
J.
,
Obst
,
O.
,
Lizier
,
J. T.
,
Mayer
,
N. M.
, and
Asada
,
M.
,
2012
, “
Information Processing in Echo State Networks at the Edge of Chaos
,”
Theory Biosci.
,
131
(
3
), pp.
205
213
.
50.
Luo
,
X. S.
,
2007
, “
Passivity-Based Adaptive Control of Chaotic Oscillations in Power System
,”
Chaos, Solitons Fractals
,
31
(
3
), pp.
665
671
.
51.
Mata-Machuca
,
J. L.
,
Martínez-Guerra
,
R.
,
Aguilar-López
,
R.
, and
Aguilar-Ibañez
,
C.
,
2012
, “
A Chaotic System in Synchronization and Secure Communications
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
4
), pp.
1706
1713
.
52.
Azzaz
,
M. S.
,
Tanougast
,
C.
,
Sadoudi
,
S.
,
Fellah
,
R.
, and
Dandache
,
A.
,
2013
, “
A New Auto-Switched Chaotic System and Its FPGA Implementation
,”
Commun. Nonlinear Sci. Numer. Simul.
,
18
(
7
), pp.
1792
1804
.
53.
Yu
,
X.
, and
Zhihong
,
M.
,
2002
, “
Fast Terminal Sliding-Mode Control Design for Nonlinear Dynamical Systems
,”
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
49
(
2
), pp.
261
264
.
54.
Hong
,
K.-S.
,
2011
, “
Synchronization of Coupled Chaotic FitzHugh–Nagumo Neurons Via Lyapunov Functions
,”
Math. Comput. Simul.
,
82
(
4
), pp.
590
603
.
55.
Kebriaei
,
H.
, and
Yazdanpanah
,
M. J.
,
2010
, “
Robust Adaptive Synchronization of Different Uncertain Chaotic Systems Subject to Input Nonlinearity
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
2
), pp.
430
441
.
56.
Mobayen
,
S.
,
2016
, “
Finite-Time Robust-Tracking and Model-Following Controller for Uncertain Dynamical Systems
,”
J. Vib. Control
,
22
(
4
), pp.
1117
1127
.
57.
Bayat
,
F.
,
Mobayen
,
S.
, and
Javadi
,
S.
,
2016
, “
Finite-Time Tracking Control of Nth-Order Chained-Form Non-Holonomic Systems in the Presence of Disturbances
,”
ISA Trans.
,
63
, pp.
78
83
.
58.
Yau
,
H.-T.
, and
Yan
,
J.-J.
,
2008
, “
Chaos Synchronization of Different Chaotic Systems Subjected to Input Nonlinearity
,”
Appl. Math. Comput.
,
197
(
2
), pp.
775
788
.
59.
Chen
,
G.
, and
Yu
,
X.
,
1999
, “
On Time-Delayed Feedback Control of Chaotic Systems
,”
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
46
(
6
), pp.
767
772
.
60.
Lin
,
T.-C.
, and
Lee
,
T.-Y.
,
2011
, “
Chaos Synchronization of Uncertain Fractional-Order Chaotic Systems With Time Delay Based on Adaptive Fuzzy Sliding Mode Control
,”
IEEE Trans. Fuzzy Syst.
,
19
(
4
), pp.
623
635
.
61.
Park
,
J.
, and
Kwon
,
O.
,
2005
, “
A Novel Criterion for Delayed Feedback Control of Time-Delay Chaotic Systems
,”
Chaos, Solitons Fractals
,
23
(
2
), pp.
495
501
.
62.
Richard
,
J.-P.
,
2003
, “
Time-Delay Systems: An Overview of Some Recent Advances and Open Problems
,”
Automatica
,
39
(
10
), pp.
1667
1694
.
63.
Zhang
,
H.
,
Ma
,
T.
,
Huang
,
G.-B.
, and
Wang
,
Z.
,
2010
, “
Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks Via Dual-Stage Impulsive Control
,”
IEEE Trans. Syst., Man, Cybern., Part B (Cybern.)
,
40
(
3
), pp.
831
844
.
64.
Al-Shamali
,
S. A.
,
Crisalle
,
O. D.
, and
Latchman
,
H. A.
,
2003
, “
An Approach to Stabilize Linear Systems With State and Input Delay
,”
American Control Conference
(
ACC
), Denver, CO, June 4–6, pp.
875
880
.
65.
Roh
,
Y.-H.
, and
Oh
,
J.-H.
,
2000
, “
Sliding Mode Control for Robust Stabilization of Uncertain Input-Delay Systems
,”
ICASE
,
2
(
2
), pp.
98
103
.http://www.ijcas.org/admin/paper/files/2-2-3.pdf
66.
Mobayen, S.
,
Takougang Kingni, S.
,
Pham, V. T.
,
Nazarimehr, F.
, and
Jafari, S.
, 2017, “
Analysis, Synchronization and Circuit Design of a New Highly Nonlinear Chaotic System
,”
Int. J. Syst. Sci.
, epub.
67.
Vaidyanathan
,
S.
,
2013
, “
Analysis and Adaptive Synchronization of Two Novel Chaotic Systems With Hyperbolic Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters
,”
J. Eng. Sci. Technol. Rev.
,
6
(
4
), pp.
53
65
.http://www.jestr.org/downloads/Volume6Issue4/fulltext7642013.pdf
68.
Mobayen
,
S.
, and
Tchier
,
F.
,
2017
, “
Composite Nonlinear Feedback Control Technique for Master/Slave Synchronization of Nonlinear Systems
,”
Nonlinear Dyn.
,
87
(
3
), pp.
1731
1747
.
69.
Nehmzow
,
U.
, and
Walker
,
K.
,
2005
, “
Quantitative Description of Robot–Environment Interaction Using Chaos Theory
,”
Rob. Auton. Syst.
,
53
(
3
), pp.
177
193
.
70.
Shahverdiev
,
E.
, and
Shore
,
K.
,
2008
, “
Chaos Synchronization Regimes in Multiple-Time-Delay Semiconductor Lasers
,”
Phys. Rev. E
,
77
(
5
), p.
057201
.
71.
Liao
,
J.-F.
, and
Sun
,
J.-Q.
,
2013
, “
Polarization Dynamics and Chaotic Synchronization in Unidirectionally Coupled VCSELs Subjected to Optoelectronic Feedback
,”
Opt. Commun.
,
295
, pp.
188
196
.
72.
Shabunin
,
A.
,
Astakhov
,
V.
,
Demidov
,
V.
,
Provata
,
A.
,
Baras
,
F.
,
Nicolis
,
G.
, and
Anishchenko
,
V.
,
2003
, “
Modeling Chemical Reactions by Forced Limit-Cycle Oscillator: Synchronization Phenomena and Transition to Chaos
,”
Chaos, Solitons Fractals
,
15
(
2
), pp.
395
405
.
73.
Zhou
,
J.
,
Huang
,
H.
,
Qi
,
G.
,
Yang
,
P.
, and
Xie
,
X.
,
2005
, “
Communication With Spatial Periodic Chaos Synchronization
,”
Phys. Lett. A
,
335
(
2
), pp.
191
196
.
74.
Mobayen
,
S.
,
2015
, “
Design of a Robust Tracker and Disturbance Attenuator for Uncertain Systems With Time Delays
,”
Complexity
,
21
(
1
), pp.
340
348
.
75.
Khan
,
A.
, and
Shahzad
,
M.
,
2013
, “
Synchronization of Circular Restricted Three Body Problem With Lorenz Hyper Chaotic System Using a Robust Adaptive Sliding Mode Controller
,”
Complexity
,
18
(
6
), pp.
58
64
.
76.
Guo
,
R.
,
2012
, “
Finite-Time Stabilization of a Class of Chaotic Systems Via Adaptive Control Method
,”
Commun. Nonlinear Sci. Numer. Simul.
,
17
(
1
), pp.
255
262
.
77.
Pisano
,
A.
, and
Usai
,
E.
,
2004
, “
Output-Feedback Control of an Underwater Vehicle Prototype by Higher-Order Sliding Modes
,”
Automatica
,
40
(
9
), pp.
1525
1531
.
78.
Rao
,
D. V.
, and
Sinha
,
N. K.
,
2013
, “
A Sliding Mode Controller for Aircraft Simulated Entry Into Spin
,”
Aerosp. Sci. Technol.
,
28
(
1
), pp.
154
163
.
79.
Song
,
Z.
,
Li
,
H.
, and
Sun
,
K.
,
2014
, “
Finite-Time Control for Nonlinear Spacecraft Attitude Based on Terminal Sliding Mode Technique
,”
ISA Trans.
,
53
(
1
), pp.
117
124
.
80.
Hsu
,
C.-F.
, and
Lee
,
B.-K.
,
2011
, “
FPGA-Based Adaptive PID Control of a DC Motor Driver Via Sliding-Mode Approach
,”
Expert Syst. Appl.
,
38
(
9
), pp.
11866
11872
.
81.
Aghababa
,
M. P.
, and
Heydari
,
A.
,
2012
, “
Chaos Synchronization Between Two Different Chaotic Systems With Uncertainties, External Disturbances, Unknown Parameters and Input Nonlinearities
,”
Appl. Math. Modell.
,
36
(
4
), pp.
1639
1652
.
82.
Mobayen
,
S.
,
2016
, “
Finite‐Time Stabilization of a Class of Chaotic Systems With Matched and Unmatched Uncertainties: An LMI Approach
,”
Complexity
,
21
(
5
), pp.
14
19
.
83.
Mobayen
,
S.
,
2015
, “
Design of LMI‐Based Global Sliding Mode Controller for Uncertain Nonlinear Systems With Application to Genesio's Chaotic System
,”
Complexity
,
21
(
1
), pp.
94
98
.
84.
Cong
,
B.
,
Chen
,
Z.
, and
Liu
,
X.
,
2014
, “
On Adaptive Sliding Mode Control Without Switching Gain Overestimation
,”
Int. J. Robust Nonlinear Control
,
24
(
3
), pp.
515
531
.
85.
Liu
,
H.
,
Lu
,
J.-A.
,
,
J.
, and
Hill
,
D. J.
,
2009
, “
Structure Identification of Uncertain General Complex Dynamical Networks With Time Delay
,”
Automatica
,
45
(
8
), pp.
1799
1807
.
86.
Liu
,
J-K.
, and
Sun
,
F-C.
,
2006
, “
Nominal Model-Based Sliding Mode Control With Backstepping for 3-Axis Flight Table
,”
Chin. J. Aeronaut.
,
19
(
1
), pp.
65
71
.
87.
Ting
,
H. C.
,
Chang
,
J. L.
, and
Chen
,
Y. P.
,
2012
, “
Output Feedback Integral Sliding Mode Controller of Time‐Delay Systems With Mismatch Disturbances
,”
Asian J. Control
,
14
(
1
), pp.
85
94
.
88.
Xia
,
Y.
,
Fu
,
M.
,
Yang
,
H.
, and
Liu
,
G.-P.
,
2009
, “
Robust Sliding-Mode Control for Uncertain Time-Delay Systems Based on Delta Operator
,”
IEEE Trans. Ind. Electron.
,
56
(
9
), pp.
3646
3655
.
89.
Yan
,
X.-G.
,
Spurgeon
,
S. K.
, and
Edwards
,
C.
,
2008
, “
Static Output Feedback Sliding Mode Control for Time-Varying Delay Systems With Time-Delayed Nonlinear Disturbances
,”
IFAC Proc.
,
41
(
2
), pp.
8642
8647
.
90.
Guo
,
L.
,
Gu
,
H.
,
Xing
,
J.
, and
He
,
X.
,
2012
, “
Asymptotic and Exponential Stability of Uncertain System With Interval Delay
,”
Appl. Math. Comput.
,
218
(
19
), pp.
9997
10006
.
91.
He
,
P.
,
Jing
,
C.-G.
,
Fan
,
T.
, and
Chen
,
C.-Z.
,
2013
, “
Robust Adaptive Synchronisation of Complex Networks With Multiple Coupling Time-Varying Delays
,”
Int. J. Autom. Control
,
7
(
4
), pp.
223
248
.
92.
Hung
,
Y.-C.
,
Yan
,
J.-J.
, and
Liao
,
T.-L.
,
2008
, “
Projective Synchronization of Chua's Chaotic Systems With Dead-Zone in the Control Input
,”
Math. Comput. Simul.
,
77
(
4
), pp.
374
382
.
93.
Pai
,
M.-C.
,
2015
, “
Chaotic Sliding Mode Controllers for Uncertain Time-Delay Chaotic Systems With Input Nonlinearity
,”
Appl. Math. Comput.
,
271
, pp.
757
767
.
94.
Pai
,
M. C.
,
2016
, “
Chaos Control of Uncertain Time‐Delay Chaotic Systems With Input Dead‐Zone Nonlinearity
,”
Complexity
,
21
(
3
), pp.
13
20
.
95.
Vaidyanathan
,
S.
, and
Sampath
,
S.
,
2011
, “
Global Chaos Synchronization of Hyperchaotic Lorenz Systems by Sliding Mode Control
,”
Advances in Digital Image Processing and Information Technology
, D. Nagamalai, E. Renault, and M. Dhanuskodi, eds.,
Springer
, Berlin, pp.
156
164
.
96.
Pai
,
M. C.
,
2010
, “
Design of Adaptive Sliding Mode Controller for Robust Tracking and Model Following
,”
J. Franklin Inst.
,
347
(
10
), pp.
1837
1849
.
97.
Chua
,
L. O.
, and
Lin
,
G.-N.
,
1990
, “
Canonical Realization of Chua's Circuit Family
,”
IEEE Trans. Circuits Syst.
,
37
(
7
), pp.
885
902
.
98.
Adloo
,
H.
,
Noroozi
,
N.
, and
Karimaghaee
,
P.
,
2012
, “
Observer-Based Model Reference Adaptive Control for Unknown Time-Delay Chaotic Systems With Input Nonlinearity
,”
Nonlinear Dyn.
,
67
(
2
), pp.
1337
1356
.
You do not currently have access to this content.