In nonlinear control, the technique of Lyapunov redesign refers to the design where a stabilizing state feedback controller can be constructed with knowledge of the Lyapunov function
V
. Consider the system
x
˙
=
f
(
t
,
x
)
+
G
(
t
,
x
)
[
u
+
δ
(
t
,
x
,
u
)
]
where
x
∈
R
n
is the state vector and
u
∈
R
p
is the vector of inputs. The functions
f
,
G
, and
δ
are defined for
(
t
,
x
,
u
)
∈
[
0
,
inf
)
×
D
×
R
p
, where
D
⊂
R
n
is a domain that contains the origin. A nominal model for this system can be written as
x
˙
=
f
(
t
,
x
)
+
G
(
t
,
x
)
u
and the control law
u
=
ϕ
(
t
,
x
)
+
v
stabilizes the system. The design of
v
is called Lyapunov redesign.
