User:Fake Proof/Sandbox/Lyapunov Function

Definition
Let $U$ be an open set of $\R^n$.

Let $f: U \to \R^n$ be a vector field.

Let $\mathbf x_0 \in U$ be an equilibrium point of the system $\mathbf x' = \map f {\mathbf x}$.

Let $V: U \to \R$ a positive definite and differentiable real-valued function.

Then $V$ is called a Lyapunov function of the system $\mathbf x' = \map f {\mathbf x}$.

Also known as
The name is sometimes seen spelt Liapunov function.