Talk:Control-Lyapunov function

$f(x)$ or $f(x,u)$?

At the start of the article, $f$ is function of the single variable $x$. And at the end is dependent of $u$ also. I think that the article should be changed to avoid this. To solve it I suppose that first equation can be changed to read:

${\dot {x}}(t)=f(x(t),\,u(t)),$

Positive definiteness of $V(x,u)$

It should be made clear if positive definiteness of $V$ is withs respect to $x$ or both $x$ and $u$. I would say for the explanation that is only for $x$, but I feel that something is missing in the explanation.