Given the ODE system $$\dot{x} = y \\ \dot{y} = \frac{1}{\alpha} (z - y)$$ where $\alpha > 0$ is a constant. How can I find a bound for $z$ depending on $x$ such that $\forall t ~x(t) \geq 0$ under suitable initial conditions ($x \geq 0$ and constraint on $z$ is met initially)? I would expect the bound to be a function $f$ such that $\forall t~ z(t) \geq f(x(t))$ must hold.
Thanks for your help.