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| − | It was mentioned in the discussion that it would be nice that a description of the mathematical notations used below was explained. So, here it is: [[Mathematical Shorthand_ECE301Fall2008mboutin]] | + | Edit: It was mentioned in the discussion that it would be nice that a description of the mathematical notations used below was explained. So, here it is: [[Mathematical Shorthand_ECE301Fall2008mboutin]] |
== Formal Definition of a Stable System == | == Formal Definition of a Stable System == | ||
Revision as of 20:00, 17 September 2008
Edit: It was mentioned in the discussion that it would be nice that a description of the mathematical notations used below was explained. So, here it is: Mathematical Shorthand_ECE301Fall2008mboutin
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}\, $ )
Comments on Other Answers
Talk:HW3-A Derek Hopper_ECE301Fall2008mboutin
