
Saunder January 22, 2014 10:43 K15053˙Book
120 Disturbance Observer-Based Control: Methods and Applications
where
A =
010··· 0
001··· 0
·······
000··· 1
−c
0
−c
1
−c
2
··· −c
ρ−1
,
M(ξ, η) =
m
1
(ξ, η)
m
2
(ξ, η)
.
.
.
m
ρ−1
(ξ, η)
−
#
ρ−1
i=1
c
i
m
i
(ξ, η)
,
N(ξ, η) =
0
0
.
.
.
0
m
ρ
(ξ, η) +
#
ρ−1
i=1
c
i
m
i
(ξ, η)
It can be obtained from (8.24) that
ξ = A
−1
˙
ξ − M(ξ, η)d − N(ξ, η)e
(8.25)
Suppose that the closed-loop system reaches a steady-state and let ξ
s
, η
s
, e
s
, and y
s
denote the steady-state values of ξ , η, e, and y , respectively. Steady-state value ξ
s
can be represented as
ξ
s
=−A
−1
[
M(ξ
s
, η
s
)d
s
+ N(ξ
s
, η
s
)e
s
]
(8.26)
Considering the fact that e
s
=