Lyapunov function: Difference between revisions

Revision as of 03:04, 2 October 2021

Revision as of 03:07, 2 October 2021

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:<math>\dot{x} = f(x).</math>

and use the notation <math>\dot{V}(x)</math> to denote the time derivative of the Lyapunov-candidate-function <math>V</math>:

:<math>\dot{V}(x) = \frac{d}{dt} V(x(t)) = \frac{\partial V}{\partial x}\cdot \frac{dx}{dt} = \nabla V \cdot \dot{x} = \nabla V\cdot f(x).</math>.

===Locally asymptotically stable equilibrium===