Lyapunov function: Difference between revisions

Revision as of 08:32, 16 August 2020

Revision as of 10:04, 26 August 2020

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:<math>\begin{cases} g : \R ^n \to \R ^n \\ \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 locallystrictly positive-definite, and for which <math>-\nabla{V}\cdot g</math> is also locallystrictly positive definite. The condition that <math>-\nabla{V}\cdot g</math> is locally positive definite is sometimes stated as <math>\nabla{V}\cdot g</math> is locally negative definite.

===Further discussion of the terms arising in the definition===