Formal Definition of a Stable System
A system is called stable if for any bounded input $ \,x(t)\, $
$ \,\exists \epsilon \in \mathbb{R}\, $ such that $ \,|x(t)|<\epsilon , \forall t\in\mathbb{R}\, $
yields a bounded output $ \,y(t)\, $.
$ \,\exists \delta \in \mathbb{R}\, $ such that $ \,|y(t)|<\delta , \forall t\in\mathbb{R}\, $
