I am sure this is a simple solution, but I just cant seem to get this solution
In sliding mode, following along with this video, https://www.youtube.com/watch?v=x9WxwM6Ebvo&list=PLv8cjLiRoYbivwv0-wZOrHTS6pbydqDOe&index=1 , the lyapunov equation $\dot V \leq -\alpha V^{1/2}$ is integrated from $0$ to $t$ and the result is somehow $V^{1/2}(t) \leq -\frac{1}{2}\alpha t + V^{1/2}(0)$
I cannot seem to get this answer, can anyone help me out? How did they get this?
You have to use separation of variables, namely the differential equation can be written as
$$ \frac{dV}{\sqrt{V}} \leq -\alpha\,dt. $$