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Lyapunov function
(
V
)
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Words: 300
Articles: 11
A Lyapunov function near an equilibrium
x
∗
is continuously differentiable, satisfies
V
(
x
∗
)
=
0
and
V
(
x
)
>
0
away from
x
∗
, and has orbital derivative
V
˙
(
x
)
=
∇
V
(
x
)
⋅
f
(
x
)
≤
0.
(27)
Table of contents
300
11
Lyapunov stability
Lyapunov function
23
First Lyapunov theorem
Lyapunov function
13
Second Lyapunov theorem
Lyapunov function
16
Asymptotic stability
Lyapunov function
19
Ellipsoidal Lyapunov function
Lyapunov function
21
Invariant sublevel set
Lyapunov function
39
1
Tangency at a Lyapunov boundary
Invariant sublevel set
23
LaSalle invariance principle
Lyapunov function
143
3
Damped mechanical energy as a Lyapunov function
LaSalle invariance principle
122
2
Damped rational double-barrier phase portrait
Damped mechanical energy as a Lyapunov function
86
1
Outward escape from the rational potential barrier
Damped rational double-barrier phase portrait
34
Ancestors
(4)
Dynamical systems
Branch of physics
Physics
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(4)
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