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A Lyapunov function for an autonomous [[dynamical system]]
:<math>\begin{cases}
\\ \dot{y} = g(y) \end{cases}</math> with an equilibrium point at <math>y=0</math> is a [[scalar function]] <math>V:\R^n\to\R</math> that is continuous, has continuous first derivatives, is strictly positive, and for which <math>-\nabla{V}\cdot g</math> is also strictly positive. The condition that <math>-\nabla{V}\cdot g</math> is strictly positive is sometimes stated as <math>-\nabla{V}\cdot g</math> is ''locally positive definite'', or <math>\nabla{V}\cdot g</math> is ''locally negative definite''.
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