(New page: == Stable System == An input is said to be bounded if it is bounded above and below for all values of t. For example, cos(t) is a bounded input since it is bounded above by 1 and below by...) |
|||
| Line 1: | Line 1: | ||
== Stable System == | == Stable System == | ||
| − | An input is said to be bounded if it is bounded above and below for all values of t. For example, cos(t) is a bounded input since it is bounded above by 1 and below by -1, while exp(t) is not a bounded input since for increasing t, the function increases without bound. A system is therefore said to be bounded if a bounded output yields a bounded input. | + | An input is said to be bounded if it is bounded above and below for all values of t. For example, cos(t) is a bounded input since it is bounded above by 1 and below by -1, while exp(t) is not a bounded input since for increasing t, the function increases without bound. A system is therefore said to be bounded if a bounded output yields a bounded input. According to Professor Boutin, mathematically this means that there exists an <math> \epsilon \!</math> such that |
| + | <math>|x(t)| < \epsilon \!</math> | ||
Revision as of 10:22, 16 September 2008
Stable System
An input is said to be bounded if it is bounded above and below for all values of t. For example, cos(t) is a bounded input since it is bounded above by 1 and below by -1, while exp(t) is not a bounded input since for increasing t, the function increases without bound. A system is therefore said to be bounded if a bounded output yields a bounded input. According to Professor Boutin, mathematically this means that there exists an $ \epsilon \! $ such that $ |x(t)| < \epsilon \! $
