Category:Lyapunov Functions

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This category contains results about Lyapunov Functions.
Definitions specific to this category can be found in Definitions/Lyapunov Functions.

Let $x_0$ be an equilibrium point of the system of differential equations $x' = \map f x$.

Then a function $V$ is a Lyapunov function of the system $x' = \map f x$ on an open set $U$ containing the equilibrium if and only if:

$(1): \quad \map V {x_0} = 0$
$(2): \quad \map V x > 0$ if $x \in U \setminus \set {x_0}$
$(3): \quad \nabla V \cdot f \le 0$ for $x \in U$.

Pages in category "Lyapunov Functions"

This category contains only the following page.