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== Formal Definition of a Stable System == | == Formal Definition of a Stable System == | ||
| + | A system is called stable if for any bounded input <math>\,x(t)\,</math> | ||
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| + | <math>\,\exists \epsilon \in \mathbb{R}\,</math> such that <math>\,|x(t)|<\epsilon , \forall t\in\mathbb{R}\,</math> | ||
| + | |||
| + | yields a bounded output <math>\,y(t)\,</math>. | ||
| + | |||
| + | <math>\,\exists \delta \in \mathbb{R}\,</math> such that <math>\,|y(t)|<\delta , \forall t\in\mathbb{R}\,</math> | ||
== Formal Definition of an Unstable System == | == Formal Definition of an Unstable System == | ||
Revision as of 15:46, 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}\, $
