
Saunder January 22, 2014 10:43 K15053˙Book
142 Disturbance Observer-Based Control: Methods and Applications
Assumption 9.3 The disturbance estimation error in (9.13) is bounded by e
∗
d
=
sup
t>0
|e
d
(t)|.
Lemma 9.2 [113] Consider a nonlinear system
˙
x = F (x, w) which is input-to-state
stable (ISS). If the input satisfies lim
t→∞
w(t) = 0, then the state lim
t→∞
x(t) = 0.
Theorem 9.1 Supposethat Assumptions9.1-9.3 are satisfiedfor system(9.1).Consider-
ing system (9.1) under proposed control law (9.12), the closed-loop system is asymptotically
stable if the switching gain in control law (9.12) is designed such that k > (c +lg
2
)e
∗
d
and observer gain l is chosen ...