(Formal Definition of a Stable System)
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== Formal Definition of a Stable System ==
 
== Formal Definition of a Stable System ==
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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>
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yields a bounded output <math>\,y(t)\,</math>.
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<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 14:46, 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}\, $

Formal Definition of an Unstable System

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