(→Formal Definition of an Unstable System) |
|||
| Line 16: | Line 16: | ||
| − | that yields | + | that yields an unbounded output <math>\,y(t)\,</math>. |
( there is no <math>\,\delta \in \mathbb{R}\,</math> such that <math>\,|y(t)|<\delta , \forall t\in\mathbb{R}\,</math> ) | ( there is no <math>\,\delta \in \mathbb{R}\,</math> such that <math>\,|y(t)|<\delta , \forall t\in\mathbb{R}\,</math> ) | ||
Revision as of 14:56, 17 September 2008
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}\, $ )
Formal Definition of an Unstable System
A system is called unstable if there exists a bounded input $ \,x(t)\, $
( $ \,\exists \epsilon \in \mathbb{R}\, $ such that $ \,|x(t)|<\epsilon , \forall t\in\mathbb{R}\, $ )
that yields an unbounded output $ \,y(t)\, $.
( there is no $ \,\delta \in \mathbb{R}\, $ such that $ \,|y(t)|<\delta , \forall t\in\mathbb{R}\, $ )
