© The Institution of Engineering and Technology
This study reconsiders the problem of reachable set bounding for a class of linear systems in the presence of both discrete and distributed delays. Some new criteria are established where the useful term is retained when we estimate the upper bound of the derivative of the Lyapunov–Krasovskii functional. The free-weighting matrix technique is utilised to realise such a purpose. Moreover, the special structure constraint on the final expression of the derivative of the Lyapunov functional in the previous result of authors is removed. Consequently, a tighter bound of the reachable set is obtained. Numerical examples are given to illustrate the merit of the proposed method comparing with the existing ones.
References
-
-
1)
-
D. Yue ,
Q. Han
.
Robust H∞ filter design of uncertain descriptor systems with discrete and distributed delays.
IEEE Trans. Signal Proc.
,
3200 -
3212
-
2)
-
E. Fridman ,
U. Shaked
.
On reachable sets for linear systems with delay and bounded peak inputs.
Automatica
,
2005 -
2010
-
3)
-
O.M. Kwon ,
S.M. Lee ,
J.H. Park
.
On the reachable set bounding of uncertain dynamic systems with time-varying delays and disturbances.
Inf. Sci.
,
3735 -
3748
-
4)
-
Y. He ,
Q.G. Wang ,
L. Xie ,
C. Lin
.
Further improvement of free-weighting matrices technique for systems with time-varying delay.
IEEE Trans. Autom. Control
,
2 ,
293 -
299
-
5)
-
P.T. Nam ,
P.N. Pathirana
.
Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays.
Automatica
,
1838 -
1841
-
6)
-
Gu, K.: `An integral inequality in the stability problem of time-delay systems', Proc. 39th IEEE Conf. on Decision and Control, 2000, p. 2805–2810.
-
7)
-
J.H. Kim
.
Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances.
Automatica
,
2940 -
2943
-
8)
-
H. Gao ,
T. Chen
.
New results on stability of discrete-time systems with time-varying state delay.
IEEE Trans. Autom. Control
,
2 ,
328 -
334
-
9)
-
Z. Zuo ,
D.W.C. Ho ,
Y. Wang
.
Reachable set estimation for linear systems in the presence of both discrete and distributed delays.
IET Control Theory Appl.
,
1808 -
1812
-
10)
-
Z. Zuo ,
D.W.C. Ho ,
Y. Wang
.
Reachable set bounding for delayed systems with polytopic uncertainties: the maximal Lyapunov-Krasovskii functional approach.
Automatica
,
949 -
952
-
11)
-
J. Hale
.
(1977)
Theory of functional differential equations.
-
12)
-
S. Xu ,
J. Lam
.
Improved delay-dependent stability criteria for time-delay systems.
IEEE Trans. Autom. Control
,
3 ,
384 -
387
-
13)
-
T. Hu ,
Z. Lin
.
(2001)
Control systems with actuator saturation: analysis and design.
-
14)
-
N. Ramdani ,
N. Meslem ,
Y. Candau
.
A hybrid bounding method for computing an over-approximation for the reachable set of uncertain nonlinear systems.
IEEE Trans. Autom. Control
,
2352 -
2364
-
15)
-
A. Kurzhanskiy ,
P. Varaiya
.
Ellipsoidal techniques for reachability analysis of discrete-time linear systems.
IEEE Trans. Autom. Control
,
26 -
38
-
16)
-
S. Boyd ,
L.E. Ghaoui ,
E. Feron ,
V. Balakrishnan
.
(1994)
Linear matrix inequalities in system and control theory.
-
17)
-
L. Xie ,
E. Fridman ,
U. Shaked
.
Robust H∞ control of distributed delay systems with application to combustion control.
IEEE Trans. Autom. Control
,
1930 -
1935
-
18)
-
C. Shen ,
S. Zhong
.
The ellipsoidal bound of reachable sets for linear neural systems with disturbances.
J. Franklin Inst.
,
2570 -
2585
-
19)
-
C. Durieu ,
E. Walter ,
B. Polyak
.
Multi-input multi-output ellipsoidal state bounding.
J. Optim. Theory Appl.
,
273 -
303
-
20)
-
T. Hu ,
Z. Lin
.
Composite quadratic lyapunov functions for constrained control systems.
IEEE Trans. Autom. Control
,
3 ,
440 -
450
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2012.0491
Related content
content/journals/10.1049/iet-cta.2012.0491
pub_keyword,iet_inspecKeyword,pub_concept
6
6