Information Technology Reference
In-Depth Information
By lemma1,
⎡
⎤
−
P
+
S
∗
∗
∗
⎣
⎦
0
−
S
∗
∗
<
0
(6)
H
2
−
C
1
−
C
2
−
H
2
−
∗
P
−
1
G
0
G
1
H
1
−
Pre-and post-multiplying the matrix (16) by diag (
I, I, I, P
−
1
) , let
X
=
P
−
1
,W
=
P
−
1
SP
−
1
,Y
=
KX
, we have inequality (7), It can be proved.
4 Numerical Example
Consider the uncertain time-delay system (1), and as is known
A
0
=
−
,A
1
=
−
14
0
10
.
5
10
.
1
−
1
B
0
=
B
1
=
0
1
,D
0
=
0
.
1
,D
1
=
0
.
1
,D
2
=
0
.
1
0
.
1
0
.
1
0
.
1
D
1
=
0
.
1
,D
2
=
0
.
1
0
.
1
0
.
1
E
0
=
0
.
20
.
3
0
.
10
.
4
,E
1
=
0
.
20
.
4
0
.
10
.
3
,E
2
=
0
.
20
.
1
0
.
30
.
4
we are known from theorem 2 using Matlab to solve
X
=
0
.
1291
,Y
=
−
0
.
4304
−
0
.
2015
0
.
1291
−
−
0
.
2015 0
.
9243
K
=
YX
−
1
=
−
1
.
0362
2
.
6174
−
thus passive controller of the system can be designed
u
(
k
)=
YX
−
1
x
(
k
)=
−
2
.
6174
x
1
(
k
)
−
1
.
0362
x
2
(
k
)
References
1. Dugard, L., Verriest, E.I.: Stability and Control of Time-delay Systems. Springer,
Berlin (1998)
2. Chen, T., Francis, B.: Optimal Sampled-Data Control System. Springer, New York
(1995)
3. Wu, J.F., Wang, Q., Chen, S.B.: Robust stability for sampled-data systems. Control
Theory & Applications 18(8), 99-102 (2001)
4. Cui, B.T., Hua, M.G.: Robust passive control for uncertain discrete-time systems
with time-varying delays. Chaos Solitons & Fractials 29(2), 331-341 (2006)
Search WWH ::
Custom Search