Theorem.
Let
Q
(
s
) be a
p
x
p
matrix of polynomials and be
represented by its row vectors
as shown:
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
p
P
P
P
Q
M
2
1
{ }
.
,
,
2
,
1
,
deg
p
i
p
P
i
i
L
=
=
Let
Then,
{
}
∑
=
≤
p
i
i
p
Q
1
deg
Q
(
s
) is said to be rowreduced if
{
}
∑
=
=
p
i
i
p
Q
1
deg
ii. ObserverForm Realization
(1) Rowreduced NonSingular Matrix of Polynomials
─
given a coprime LMFD,
G
(
s
)=
Q
L

1
P
L
.
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Ex.
⎥
⎦
⎤
⎢
⎣
⎡
+
+
−
=
1
1
1
)
(
2
3
s
s
s
s
s
Q
p
1
=3
{
}
{
}
.
,
5
2
3
2
1
)
1
(
1
deg
deg
2
1
2
2
3
reduced
row
not
p
s
s
s
s
s
s
Q
i
i
−
=
+
=
<
=
−
−
−
=
+
+
−
−
=
∑
=
p
2
=2
Definition.
Let
Q
(
s
) be a
p
x
p
matrix of polynomials and be
represented by its row vectors as shown:
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
p
P
P
P
Q
M
2
1
{ }
.
,
,
2
,
1
,
deg
p
i
p
P
i
i
L
=
=
Let
be the coefficient row vector of
terms
in
P
i
,
i
= 1, 2, ...,
p
.
i
w
r
i
p
s
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
p
def
hr
w
w
w
Q
r
M
r
r
2
1

the highestrowdegree coefficient matrix.
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