
Saunder January 22, 2014 10:43 K15053˙Book
76 Disturbance Observer-Based Control: Methods and Applications
V
c
(x) such that its derivative along system (5.13) satisfies
˙
V
c
(x) =
∂V
c
(x)
∂x
( f (x) + g
1
(x)β(x)) < −δ
1
||x|| (5.16)
where δ
1
is a small positive scalar. Taking
V(x, e) = V
c
(x) +µV
o
(e) = V
c
(x) +µe
T
Pe (5.17)
as a Lyapunov candidate for system (5.15) where µ is a large positive scalar to be
determined, one obtains
˙
V
c
(x) =
∂V
c
(x)
∂x
( f (x) + g
1
(x)β(x) + g
2
(x)e
1
) +2µe
T
(A − l(x)g
2
(x)C)e.
(5.18)
The global exponential stability of disturbance observer error system indicates that
˙
V
o
(e) < −δe
T
e, (5.19)
for any x and e.
Since transfer function (5.9) is asymptotically ...