Liapunov's Stability Theorem
Theorem
Let $V$ be a Liapunov function on an open set containing an equilibrium point $x_0$.
In what context is open set to be taken?
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Then $x_0$ is stable.
If $V$ is strict, then $x_0$ is asymptotically stable.
Proof
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Source of Name
This entry was named for Aleksandr Lyapunov.
