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In-Depth Information
0
1
K
i
nx
n
1
3
.K
i
Cx
3
/
2
K
M
.K
M
Cx
1
/
2
v
m
0
@
A
J D
v
d
K
d
.K
d
Cx
2
/
2
K
1
(3.38)
0
K
2
0
K
1
K
2
The associated characteristic polynomial is
C Œ
v
K
d
C K
1
C K
2
C
v
m
C Œ
K
2
v
d
K
d
K
M
.
v
K
d
/ C K
1
C K
2
C
v
M
v
M
K
M
K
2
v
d
K
d
:
(3.39)
The variation ranges for parameter K
d
are taken to be K
d
2ŒK
mi
d
;K
ma
d
D
Œ0:4;0:9. Then the variation ranges of the rest of the parameters of the characteristic
polynomial are: c
2
D Œ
v
K
d
C K
1
C K
2
C
p./D
3
K
M
2
C
v
M
K
M
2Œ3:59;5:54, c
1
D
K
2
v
d
K
d
K
M
.
v
K
d
/ C
v
M
C
v
M
K
M
K
2
v
d
K
1
C K
2
2Œ3:42;6:41 and c
0
D
K
d
2Œ0:88;1:97.
Next, the four Kharitonov polynomials are computed as follows:
p
1
./ D c
max
C c
ma
1
C c
mi
2
2
C c
mi
3
3
0
p
2
./ D c
min
C c
mi
1
C c
ma
2
2
C c
ma
3
3
0
(3.40)
p
3
./ D c
min
C c
ma
1
C c
ma
2
2
C c
mi
3
3
0
p
4
./ D c
max
C c
mi
1
C c
mi
2
2
C c
ma
3
3
0
which take the values
p
1
./ D 1:97 C 6:41 C 3:59
2
C
3
p
2
./ D 0:88 C 3:42 C 5:54
2
C
3
(3.41)
p
3
./ D 0:88 C 6:41 C 5:54
2
C
3
p
4
./ D 1:97 C 3:42 C 3:59
2
C
3
The Routh criterion is applied for each characteristic polynomial p
i
./ i
D
1; ;4. For polynomial p
1
./ it holds
3
j 1 6:41
2
j 3:59 1:97
(3.42)
1
j 5:86 0
0
j 1:97
Since there is no change of sign in the first column of the Routh matrix it can be
concluded that the characteristic polynomial is a stable one. For polynomial p
2
./
it holds
3
j 1 3:42
2
j 5:54 0:88
(3.43)
1
j 3:26 0
0
j 0:88
