Category:Definitions/Lyapunov Functions
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This category contains definitions related to Lyapunov Functions.
Related results can be found in Category: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 "Definitions/Lyapunov Functions"
The following 5 pages are in this category, out of 5 total.