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In compliance with the work [5] the sought for matrix
L
=
L
0
∈
R
m
×
n
is calculated by recursive formulas
L
J
=
B
+
J
A
J
−
Φ
J
B
+
J
;
L
k
=
B
−
k
A
k
−
Φ
k
B
−
k
;
B
−
k
=
L
k
+1
B
⊥
k
+
B
+
k
, k
= 0
, J
−
1
,
and provides the exact set pole placement. This is actually so, as all
elements of the set of eigenvalues
eig (
A
−
LC
)
correspond to eigenvalues
of a set of stable matrices
Φ
i
, of the size
m
×
m
,
i
= 0
, J
. Here
B
+
0
, . . . , B
+
J
are pseudo reverse matrices of Moor – Penrose. Thus, for the synthesis of
the observer of a full rank order considered hereit is necessary:
1) to conduct a linear approximation for further using the observer
synthesis algorithm for linear systems [7];
2) to use the following synthesis algorithm for full rank state observer:
— set the matrices
A
0
=
A
T
;
B
0
=
C
T
— calculate
J
= ceil
n
m
−
1;
— set the matrices
Φ = Φ
0
,
Φ
1
, . . . ,
Φ
J
so that the desired spectre of
the state observer comprises
J
+1
[
i
=1
eig (Φ
i
−
1
) ;
— define the ortogonal annihilator
B
⊥
k
−
1
and then matrices
A
k
=
B
⊥
k
−
1
A
k
−
1
B
⊥
T
k
−
1
;
B
k
=
B
⊥
k
−
1
A
k
−
1
B
k
−
1
, k
= 1
, J
;
— consecutively calculate the matrices
L
т
J
= Φ
J
B
+
J
−
B
+
J
A
J
;
B
−
k
=
B
+
k
−
L
т
k
+1
B
⊥
k
;
L
т
k
= Φ
k
B
−
k
−
B
−
k
A
k
, k
=
J
−
1
,
0
.
(3)
The SC angular velocity estimation by the local vertical sensor
results.
The SC movement as a solid body around the centre of mass is
ISSN 0236-3933. HERALD of the BMSTU. Series “Instrument Engineering”. 2014. No. 5
5