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n-th order derivatives of d
i
and the associated initial conditions. Without loss of
generality it will be considered that n D 2. This means
d
1
D f
a
.y
1
; y
1
;y
2
; y
2
/
d
2
D f
b
.y
1
; y
1
;y
2
; y
2
/
(4.98)
By defining the additional state variables
z
5
D d
1
,
z
6
D d
1
,
z
7
D d
2
,
z
8
D d
2
one
has
z
1
D
z
2
,
z
2
D
v
1
C d
1
,
z
3
D
z
4
,
z
4
D
v
2
C d
2
,
z
5
D
z
6
,
z
6
D f
a
,
z
7
D
z
8
and
z
8
D f
b
. Thus, in the case of additive input disturbances the state-space equations
of the model of the coupled neurons can be written in the following matrix form
z
D
Az
C
Bv
z
m
D
Cz
(4.99)
where the state vector is
z
D Œ
z
1
;
z
2
;
z
3
;
z
4
;
z
5
;
z
6
;
z
7
;
z
8
T
, the control input vector is
u
D Œ
v
1
;
v
2
;f
a
;f
b
T
, and the measured output is
z
m
D Œ
z
1
;
z
3
T
, while matrices A,
B, and C are defined as
0
1
0
1
01000000
00001000
00010000
00000010
00000100
00000000
00000001
00000000
0000
1000
0000
0100
0000
0010
0000
0001
@
A
@
A
A D
B D
(4.100)
10000000
00100000
C D
(4.101)
The associated disturbance observer is
z
D A
o
z
C B
o
u
C K.
z
m
z
m
/
z
m
D C
o
z
(4.102)
where A
o
D A, C
o
D C and
01000000
00010000
B
o
D
(4.103)
where now
u
D Œ
u
1
;
u
2
T
.
