The problem of absolute stability for a class of neutral-type Lurie control system with nonlinearity located in an infinite sector and in a finite one is investigated in this paper. Based on the delayed-decomposition approach (DDA), a new augmented Lyapunov functional is constructed and the delay dependent conditions for asymptotic stability are derived by applying an integral inequality approach (IIA) in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.

Issue Section:
Research Papers
Keywords:
Control theory, Nonlinear systems, Uncertain systems , Control, Robust control
Topics:
Delays, Stability, Theorems (Mathematics), Control systems

References

1.
Boyd
,
S.
,
Ghaoui
,
L. E.
,
Feron
,
E.
, and
Balakrishnan
,
V.
,
1994
,
Linear Matrix Inequalities in System and Control Theory
,
SIAM
,
Philadelphia
.
2.
Dey
,
R.
,
Ghosh
,
S.
,
Ray
,
G.
, and
Rakshit
,
A.
,
2011
, “
State Feedback Stabilization of Uncertain Linear Time-Delay Systems: A Nonlinear Matrix Inequality Approach
,”
Numer. Linear Algebra Appl.
,
18
(
3
), pp.
351
–
361
.10.1002/nla.731
3.
Dugard
,
L.
, and
Verriest
,
E. I.
,
1998
,
Stability and Control of Time-Delay Systems
,
Springer
,
London
.
4.
Fridman
,
E.
,
2001
, “
New Lyapunov–Krasovskii Functionals for Stability of Linear Retarded and Neutral Type Systems
,”
Syst. Control Lett.
,
43
(
4
), pp.
309
–
319
.10.1016/S0167-6911(01)00114-1
5.
Gahinet
,
P.
,
Nemirovskii
,
A.
,
Laub
,
A. J.
, and
Chilali
,
M.
,
1995
,
LMI Control Toolbox
,
MathWorks
,
Natick, MA
.
6.
Gu
,
K.
,
2000
, “
An Integral Inequality in the Stability Problem of Time-Delay Systems
,”
39th IEEE Control Decision Conference
, Sydney, Australia, pp.
2805
–
2810
.
7.
Gu
,
K.
,
Kharitonov
,
V. L.
, and
Chen
,
J.
,
2003
,
Stability of Time-Delay Systems
,
Springer-Verlag
,
New York
.
8.
Han
,
Q.
,
2007
, “
On Designing Time-Varying Feedback Controllers for Master–Slave Synchronization of Lurie Systems
,”
IEEE Trans. Circuits Syst. I
,
54
(
7
), pp.
1573
–
1583
.10.1109/TCSI.2007.899627
9.
He
,
Y.
,
Wu
,
M.
,
She
,
J. H.
, and
Liu
,
G. P.
,
2004
, “
Parameter-Dependent Lyapunov Functional for Stability of Time-Delay Systems With Polytopictype Uncertainties
,”
IEEE Trans. Autom. Control
,
49
(
5
), pp.
828
–
832
.10.1109/TAC.2004.828317
10.
He
,
Y.
,
Wang
,
Q. G.
,
Xie
,
L. H.
, and
Lin
,
C.
,
2007
, “
Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay
,”
IEEE Trans. Autom. Control
,
52
(
2
), pp.
293
–
299
.10.1109/TAC.2006.887907
11.
Kolmanovskii
,
V. B.
, and
Myshkis
,
A. D.
,
1992
,
Applied Theory of Functional Differential Equations
,
Kluwer Academic Publishers
,
Dordrecht, The Netherlands
.
12.
Liu
,
P. L.
,
2012
, “
A Delay Decomposition Approach to Stability Analysis of Uncertain Systems With Time-Varying Delays
,”
ISA Trans.
,
51
(
6
), pp.
694
–
701
.10.1016/j.isatra.2012.07.001
13.
Liu
,
P. L.
,
2013
, “
State Feedback Stabilization of Time-Varying Delay Uncertain Systems: A Delay Decomposition Approach
,”
Linear Algebra Appl.
,
438
(
5
), pp.
2188
–
2209
.10.1016/j.laa.2012.10.008
14.
Mathiyalagan
,
K.
,
Sakthivel
,
R.
, and
Anthoni
,
S. M.
,
2011
, “
New Stability and Stabilization Criteria for Fuzzy Neural Networks With Various Activation Functions
,”
Phys. Scr.
,
84
(
1
), p.
015007
.10.1088/0031-8949/84/01/015007
15.
Mukhija
,
P.
,
Kar
,
I. N.
, and
Bhatt
,
R. K. P.
,
2014
, “
Robust Absolute Stability Criteria for Uncertain Lurie System With Interval Time-Varying Delay
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
4
), p.
041020
.10.1115/1.4026872
16.
Niculescu
,
S. I.
,
2001
,
Delay Effects on Stability: A Robust Control Approach
,
Springer
,
Berlin
.
17.
Popov
,
V. M.
, and
Halanay
,
A.
,
1962
, “
Absolute Stability of Nonlinear Controlled Systems With Delay
,”
Autom. Remote Control
,
23
(
7
), pp.
849
–
851
.
18.
Sakthivel
,
R.
,
Mathiyalagan
,
K.
, and
Anthoni
,
S. M.
,
2012
, “
Robust H∞ Control for Uncertain Discrete-Time Stochastic Neural Networks With Time-Varying Delays
,”
IET Control Theory Appl.
,
6
(
9
), pp.
1220
–
1228
.10.1049/iet-cta.2011.0254
19.
Sakthivel
,
R.
,
Karthik Raja
,
U.
,
Mathiyalagan
,
K.
, and
Leelamani
,
A.
,
2012
, “
Design of a Robust Controller on Stabilization of Stochastic Neural Networks With Time Varying Delays
,”
Phys. Scr.
,
85
(
3
), p.
035003
.10.1088/0031-8949/85/03/035003
20.
Sakthivel
,
R.
,
Vadivel
,
P.
,
Mathiyalagan
,
K.
, and
Arunkumar
,
A.
,
2014
, “
Fault-distribution Dependent Reliable H∞ Control for Takagi–Sugeno Fuzzy Systems
,”
ASME J. Dyn. Syst. Meas. Control
,
136
(
2
), p.
021021
.10.1115/1.4025987
21.
Shao
,
H. Y.
,
2008
, “
Improved Delay-Dependent Globally Asymptotic Stability Criteria for Neural Networks With a Constant Delay
,”
IEEE Trans. Circuits Syst. II
,
55
(
10
), pp.
1071
–
1075
.10.1109/TCSII.2008.2001981
22.
Vadivel
,
P.
,
Sakthivel
,
R.
,
Mathiyalagan
,
K.
, and
Thangaraj
,
P.
,
2012
, “
Robust Stabilization of Non-Linear Uncertain Takagi–Sugeno Fuzzy Systems by H∞ Control
,”
IET Control Theory Appl.
,
6
(
16
), pp.
2556
–
2566
.10.1049/iet-cta.2012.0626
23.
Brayton
,
R. K.
,
1966
, “
Bifurcation of Periodic Solutions in a nonlinear Difference-Differential Equation of Neutral Type
,”
Q. Appl. Math.
,
24
, pp.
215
–
224
.
24.
Chen
,
J. D.
,
Lien
,
C. H.
,
Fan
,
K. K.
, and
Chou
,
J. H.
,
2001
, “
Criteria for Asymptotic Stability of a Class of Neutral Systems Via a LMI Approach
,”
IEE Proc. Control Theory Appl.
,
148
(
6
), pp.
442
–
447
.10.1049/ip-cta:20010772
25.
Gao
,
J. F.
,
Su
,
H. Y.
,
Ji
,
X. F.
, and
Chu
,
J.
,
2008
, “
Stability Analysis for a Class of Neutral Systems With Mixed Delays and Sector-Bounded Nonlinearity
,”
Nonlinear Anal. Real World Appl.
,
9
(
5
), pp.
2350
–
2360
.10.1016/j.nonrwa.2007.07.003
26.
He
,
Y.
,
Wu
,
M.
,
She
,
J. H.
, and
Liu
,
G. P.
,
2004
, “
Delay-Dependent Robust Stability Criteria for Uncertain Neutral Systems With Mixed Delays
,”
Syst. Control Lett.
,
51
(
1
), pp.
57
–
65
.10.1016/S0167-6911(03)00207-X
27.
He
,
Y.
,
Wang
,
Q. G.
,
Lin
,
C.
, and
Wu
,
M.
,
2005
, “
Augmented Lyapunov Functional and Delay-Dependent Stability Criteria for Neutral Systems
,”
Int. J. Robust Nonlinear Control
,
15
(
18
), pp.
923
–
933
.10.1002/rnc.1039
28.
Liu
,
P. L.
,
2013
, “
A Delay Decomposition Approach to Stability Analysis of Neutral Systems With Time-Varying Delay
,”
Appl. Math. Model.
,
37
(
7
), pp.
5013
–
5026
.10.1016/j.apm.2012.10.007
29.
Liu
,
X. G.
,
Wu
,
M.
,
Martin
,
R.
, and
Tang
,
M. L.
,
2007
, “
Delay-Dependent Stability Analysis for Uncertain Neutral Systems With Time-Varying Delays
,”
Math. Comput. Simul.
,
75
(
1
), pp.
15
–
27
.10.1016/j.matcom.2006.08.006
30.
Liu
,
X. G.
,
Wu
,
M.
,
Martin
,
R.
, and
Tang
,
M. L.
,
2007
, “
Stability Analysis for Neutral Systems With Mixed Delays
,”
J. Comput. Appl. Math.
,
202
(
2
), pp.
478
–
497
.10.1016/j.cam.2006.03.003
31.
Park
,
J. H.
,
2002
, “
Stability Criterion for Neutral Differential Systems With Mixed Multiple Time-Varying Delay Arguments
,”
Math. Comput. Simul.
,
59
(
5
), pp.
401
–
412
.10.1016/S0378-4754(01)00420-7
32.
Ramakrishnan
,
K.
, and
Ray
,
G.
,
2012
, “
An Improved Delay-Dependent Stability Criterion for a Class of Lur'e Systems of Neutral-Type
,”
ASME J. Dyn. Syst. Meas. Control
,
134
(
1
), p.
011008
.10.1115/1.4005276
33.
Sakthivel
,
R.
,
Mathiyalagan
,
K.
, and
Anthoni
,
S. M.
,
2012
, “
Robust Stability and Control for Uncertain Neutral Time Delay Systems
,”
Int. J. Control
,
85
(
4
), pp.
373
–
383
.10.1080/00207179.2011.653832
34.
Wang
,
Y. T.
,
Zhang
,
X.
, and
He
,
Y.
,
2012
, “
Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Mixed Neutral and Lurie Dynamical Systems With Interval Time-Varying Delays and Sector-Bounded Nonlinearity
,”
Nonlinear Anal. Real World Appl.
,
13
(
8
), pp.
2188
–
2194
.10.1016/j.nonrwa.2012.01.014
35.
Wu
,
M.
,
He
,
Y.
, and
She
,
J. H.
,
2004
, “
New Delay-Dependent Stability Criteria and Stabilizing Method for Neutral Systems
,”
IEEE Trans. Autom. Control
,
49
(
12
), pp.
2266
–
2271
.10.1109/TAC.2004.838484
36.
Yin
,
C.
,
Zhong
,
S. M.
, and
Chen
,
W. F.
,
2010
, “
On Delay-Dependent Robust Stability of a Class of Uncertain Mixed Neutral and Lurie Dynamical Systems With Interval Time-Varying Delays
,”
J. Franklin Inst.
,
347
(
9
), pp.
1623
–
1642
.10.1016/j.jfranklin.2010.06.011
37.
Cao
,
J. W.
, and
Zhong
,
S. M.
,
2007
, “
New Delay-Dependent Condition for Absolute Stability of Lurie Control Systems With Multiple Time-Delays and Nonlinearities
,”
Appl. Math. Comput.
,
194
(
1
), pp.
250
–
258
.10.1016/j.amc.2007.04.034
38.
Cao
,
J. W.
,
Zhong
,
S. M.
, and
Hu
,
Y. Y.
,
2008
, “
Delay-Dependent Condition for Absolute Stability of Lurie Control Systems With Multiple Time Delays and Nonlinearities
,”
J. Math. Anal. Appl.
,
338
(
1
), pp.
497
–
504
.10.1016/j.jmaa.2007.05.039
39.
Chen
,
D. Y.
, and
Liu
,
W. H.
,
2005
, “
Delay-Dependent Robust Stability for Lurie Control Systems With Multiple Time Delays
,”
Control Theory Appl.
,
22
(
3
), pp.
499
–
502
.
40.
He
,
Y.
,
Wu
,
M.
,
She
,
J. H.
, and
Liu
,
G. P.
,
2005
, “
Robust Stability for Delay Lurie Control Systems With Multiple Nonlinearities
,”
J. Comput. Appl. Math.
,
176
(
2
), pp.
371
–
380
.10.1016/j.cam.2004.07.025
41.
Nian
,
X. H.
,
1999
, “
Delay Dependent Conditions for Absolute Stability of Lurie Type Control Systems
,”
Acta Autom. Sinica
,
25
(
4
), pp.
556
–
564
.
42.
Park
,
P.
,
1997
, “
A Revisited Popov Criterion for Nonlinear Lurie Systems With Sector Restrictions
,”
Int. J. Control
,
68
(
3
), pp.
461
–
469
.10.1080/002071797223479
43.
Qiu
,
F.
,
Cui
,
B. T.
, and
Ji
,
Y.
,
2010
, “
Delay-Dividing Approach for Absolute Stability of Lurie Control System With Mixed Delays
,”
Nonlinear Anal. Real World Appl.
,
11
(
4
), pp.
3110
–
3120
.10.1016/j.nonrwa.2009.11.006
44.
Tian
,
J. K.
,
Zhong
,
S. M.
, and
Xiong
,
L. L.
,
2007
, “
Delay-Dependent Absolute Stability of Lurie Control Systems With Multiple Time-Delays
,”
Appl. Math. Comput.
,
188
(
1
), pp.
379
–
384
.10.1016/j.amc.2006.09.119
45.
Xu
,
B. J.
, and
Liao
,
X. X.
,
2002
, “
Absolute Stability Criteria of Delay-Dependent for Lurie Control Systems
,”
Acta Autom. Sinica
,
28
(
2
), pp.
317
–
320
.
46.
Yang
,
B.
, and
Chen
,
M. Y.
,
2001
, “
Delay-Dependent Criterion for Absolute Stability of Lurie Type Control Systems With Time Delays
,”
Control Theory Appl.
,
18
(
6
), pp.
929
–
931
.
Copyright © 2015 by ASME
You do not currently have access to this content.