
Saunder January 22, 2014 10:43 K15053˙Book
Advanced Nonlinear Disturbance Observer 63
An extended high gain observer for system (4.23) is then designed as [7]
˙
ˆ
x = A
ˆ
x + B
ˆ
b(
ˆ
x) +
ˆ
a(
ˆ
x)u +
ˆ
x
n+1
+ H(ε)(y − C
ˆ
x),
˙
ˆ
x
n+1
=
α
n+1
ε
n+1
(y − C
ˆ
x),
(4.29)
where
ˆ
a(·) ≥ a
0
> 0 and
ˆ
b(·) are twice continuously differentiable and globally
bounded functions, respectively. H(ε)isdesigned as
H(ε) =
α
1
ε
, ···,
α
n
ε
n
T
,
where ε>0isasmall constant, and α
1
, ... , α
n
, α
n+1
are chosen such that the
polynomial
s
n+1
+ α
1
s
n
+···+α
n
s +α
n+1
is Hurwitz.
The corresponding output-feedback based control law is designed as
u =
−
ˆ
x
n+1
−
ˆ
b(
ˆ
x) +φ(
ˆ
x)
ˆ
a(
ˆ
x)
=
ψ(
ˆ
x,
ˆ
x
n+1
). (4.30)
However, from the high-gain ...