Given a function $x(t)$, I am looking for a function $y(t)$ which closely follows $x(t)$ except that its derivative must be bounded by a constant $c$, i.e. $\dot{y} \leq c$. Is there a way to describe $y(t)$ as ODE?
EDIT: Is there a way to design a low pass filter for $x(t)$ such that the derivative of the resulting function is bounded by $c$ everywhere?
EDIT2: Since my question is not very well formulated, I asked a more precise question here.
I appreciate your hints.