Talk:Lyapunov function: Difference between revisions

Revision as of 05:27, 24 February 2021

Revision as of 05:29, 24 February 2021

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== Definition ==

I’d say this definition is wrong: strictly positive and locally positive definite are completely different. ThisThe function <math>-\nabla{V}\cdot g</math> is not strictly positive. In particular it is zero when g is zero. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/82.35.206.78|82.35.206.78]] ([[User talk:82.35.206.78#top|talk]]) 05:26, 24 February 2021 (UTC)</small> <!--Autosigned by SineBot-->

I think that http://mathworld.wolfram.com/LyapunovFunction.html gives a much better definition than the one provided by http://planetmath.org/?op=getobj&from=objects&id=4386 . The planetmath definition does not specifiy that V is a ''scalar'' function, and it uses an example in only two independent variables (x,y) when in general V is a function in n variables. Also it is proving instability when the much more common utility of a Lyapunov function is to prove stability. I would say that the planetmath "definition" is really more of an example than a definition.