
Saunder January 22, 2014 10:43 K15053˙Book
100 Disturbance Observer-Based Control: Methods and Applications
(ii) The vector-valued function p(x) is chosen such that observer error system (7.4) is
globally asymptotically stable.
(iii) There exists a disturbance compensation gain β(x) such that G(x) = g
2
(x) +
g
1
(x)β(x) is continuously differentiable.
Proof Combining system (7.1), composite control law (7.5), and disturbance
estimation error function (7.4) together, the closed-loop system is obtained
˙
x = [ f (x) + g
1
(x)α(x)] − g
1
(x)β(x)e +[g
2
(x) + g
1
(x)β(x)]d,
˙
e =−
∂p(x)
∂x
g
2
(x)e.
(7.15)
Combining Equations (7.13), (7.14) with (7.15), the closed-loop ...