© The Institution of Engineering and Technology
This study is concerned with the stability problem for uncertain discrete-time systems with interval time-varying delays. By construction of an augmented Lyapunov–Krasovskii’s functional and utilisation of new zero equalities, improved delay-dependent criteria for the stability of the systems are derived for guaranteeing the asymptotic stability of the concerned systems. The effectiveness and the reduced conservatism of the derived results are demonstrated by three illustrative examples.
References
-
-
1)
-
S. Xu ,
J. Lam
.
A survey of linear matrix inequality techniques in stability analysis of delay systems.
Int. J. Syst. Sci.
,
1095 -
1113
-
2)
-
J.P. Richard
.
Time-delay systems: an overview of some recent advances and open problems.
Automatica
,
1667 -
1694
-
3)
-
J.-M. Jiao
.
Robust stability and Stabilisation of discrete singular systems with interval time-varying delay and linear fractional uncertainty.
Int. J. Automot. Comput.
,
8 -
15
-
4)
-
M.C. Oliveira ,
R. Skelton ,
S.O.R. Moheimani
.
(2001)
Stability tests for constrained linear systems.
-
5)
-
H. Gao ,
J. Lam ,
C. Wang ,
Y. Wang
.
Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay.
IEE Proc. Control Theory Appl.
,
6 ,
691 -
698
-
6)
-
H. Gao ,
T. Chen
.
New results on stability of discrete-time systems with time-varying state delay.
IEEE Trans. Autom. Control
,
2 ,
328 -
334
-
7)
-
P. Park ,
J.W. Ko ,
C. Jeong
.
Reciprocally convex approach to stability of systems with time-varying delays.
Automatica
,
1 ,
235 -
238
-
8)
-
P. Park
.
A delay-dependent stability criterion for systems with uncertain time-invariant delays.
IEEE Trans. Automat. Control
,
876 -
877
-
9)
-
X. Meng ,
J. Lam ,
B. Du ,
H. Gao
.
A delay-partitioning approach to the stability analysis of discrete-time systems.
Automatica
,
3 ,
610 -
614
-
10)
-
J.-H. Kim
.
Note on stability of linear systems with time-varying delay.
Automatica
,
2118 -
2121
-
11)
-
H.Y. Shao ,
Q.-L. Han
.
New stability criteria for linear discrete time systems with interval-like time-varying delays.
IEEE Trans. Autom. Control
,
3 ,
619 -
625
-
12)
-
S. Lakshmanan ,
T. Senthilkumar ,
P. Balasubramaniam
.
Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations.
Appl. Math. Model.
,
5355 -
5368
-
13)
-
C. Peng
.
Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality.
IET Control Theory Appl.
,
3 ,
448 -
453
-
14)
-
C.-H. Lien ,
K.-W. Yu ,
Y.-J. Chung ,
H.-C. Chang
.
Exponential stability and robust ℋ∞ control for uncertain discrete switched systems with interval time-varying delay.
IMA J. Math. Control Inf.
,
1 ,
121 -
141
-
15)
-
S. Boyd ,
L.E. Ghaoui ,
E. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequalities in system and control theory.
-
16)
-
S.H. Kim
.
Improved approach to robust H∞ stabilisation of discrete-time T–S fuzzy systems with time-varying delays.
IEEE T. Fuzzy Syst.
,
1008 -
1015
-
17)
-
X. Li ,
H. Gao
.
A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis.
IEEE Trans. Autom. Control
,
9 ,
2172 -
2178
-
18)
-
H. Huang ,
G. Feng
.
Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay.
IET Control Theory Appl.
,
10 ,
2152 -
2159
-
19)
-
C.-Y. Kao
.
On stability of discrete-time LTI systems with varying time delays.
IEEE Trans. Autom. Control
,
5 ,
1243 -
1248
-
20)
-
O.M. Kwon ,
J.H. Park
.
On improved delay-dependent robust control for uncertain time-delay systems.
IEEE Trans. Autom. Control
,
11 ,
1991 -
1995
-
21)
-
K. Ramakrishnan ,
Q.-L. Hang ,
G. Ray
.
Robust stability criteria for a class of uncertain discrete-time systems with time-varying delay.
Appl. Math. Model.
-
22)
-
S.-I. Niculescu
.
(2002)
Delay effects on stability: a robust approach.
-
23)
-
J. Liu ,
J. Zhang
.
Note on stability of discrete-time time-varying delay systems.
IET Control Theory Appl.
,
2 ,
335 -
339
-
24)
-
S. Xu ,
J. Lam ,
Y. Zou
.
Simplified descriptor system approach to delay-dependent stability and performance analysis for time-delay systems.
IEE Proc. Control Theory Appl.
,
2 ,
147 -
151
-
25)
-
B.Y. Zhang ,
S.Y. Xu ,
Y. Zhou
.
Improved stability criterion and its applications in delayed controller design for discrete time systems.
Automatica
,
2963 -
2967
-
26)
-
Zhu, X., Yang, G.: `Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay', Proc. American Control Conf., June 2008, Seattle, WA, p. 1644–1649.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2012.0257
Related content
content/journals/10.1049/iet-cta.2012.0257
pub_keyword,iet_inspecKeyword,pub_concept
6
6