
System with Finite Time Restrained ◾ 131
∏
∑
=µ +−µµ−
=
=
−
=
+
ji
j
i
i
n
(0)[1()] (1
2
0
2
2
1
3
,
the following conclusion is easily proven:
|D
1
| + |D
2
| = 1.
According to Reference [84], the necessary and sufficient conditions for estab-
lishment of an equal sign in │D
3
║D
1
│ + │D
4
║D
2
│ ≤ 1 are as follows:
1. All vectors expressed by λ(0)e
−bw
and
∏
−λ λ−
−
=
−
jie
biw
j
i
[1 ()]( 1)
0
2
(i = 2, 3, …,
n
1
+ 1) are collinear with the same direction.
2. All vectors expressed by μ
1
(0)e
−bw
and
−µ µ−
−
=
−
jie
biw
j
i
[1 ()]( 1)
11
0
2
(i = 2, 3, …,
n
2
+ 1) are collinear with the same direction.
3. All vectors expressed by μ
2
(0)e
−bw
and
−µ µ−
−
=
−
jie
biw
j
i
[1 ()]( 1)
22
0
2
(i