(New page: == Formal Definition for a Stable System== A system is stable if for all input functions x(t) there exists an output y(t) where y(t) is less than a constant M (Bounded inputs yield bounded...) |
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== Formal Definition for a Stable System== | == Formal Definition for a Stable System== | ||
| − | A system is stable if for all input functions x(t) there exists an output y(t) where y(t) is less than a constant M (Bounded inputs yield bounded outputs, system does not approach infinity) | + | A system is stable if for all bounded input functions x(t)(system approaches +/- infinity) there exists an output y(t) where y(t) is less than a constant M (Bounded inputs yield bounded outputs, system does not approach infinity) |
== Formal Definition for a Non-Stable System== | == Formal Definition for a Non-Stable System== | ||
| − | A system is not stable if there always exists an input x(t) such that the absolute value of the output y(t) is greater than any y(t) calculated thus far. | + | A system is not stable if there always exists an bounded input x(t) such that the absolute value of the output y(t) is greater than any y(t) calculated thus far. |
Latest revision as of 13:51, 19 September 2008
Formal Definition for a Stable System
A system is stable if for all bounded input functions x(t)(system approaches +/- infinity) there exists an output y(t) where y(t) is less than a constant M (Bounded inputs yield bounded outputs, system does not approach infinity)
Formal Definition for a Non-Stable System
A system is not stable if there always exists an bounded input x(t) such that the absolute value of the output y(t) is greater than any y(t) calculated thus far.
