Majority of nonlinear control textbooks state the following theorem:
It explicitly states that the Lyapunov function $V(\cdot)$ must be zero at the origin and positive elsewhere, yet I came across some people state that the value at the origin doesn't matter. For example,
$$ V(x_1,x_2) = x^2_1+x^2_2-1 $$ is valid Lyapunov function. My question is which one is right? Could you please also cite some reference?