Lyapunov's Stability Theorem

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Theorem

Let $V$ be a Lyapunov function on an open set containing an equilibrium point $x_0$.

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Then $x_0$ is stable.

If $V$ is strict, then $x_0$ is asymptotically stable.

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Proof

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Source of Name

This entry was named for Aleksandr Mikhailovich Lyapunov.