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| Here are some important things that you need to remember to get a nice looking bathroom after remodeling. <br><br>
| | In [[control theory]], it is often required to check if a [[nonautonomous system]] is stable or not. To cope with this it is necessary to use some special [[comparison function | comparison functions]]. Class <math>\mathcal{K}</math> functions belong to this family: |
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| | '''Definition''': a continuous function <math>\alpha : [0, a) \rightarrow [0, \infty)</math> is said to belong to class <math>\mathcal{K}</math> if: |
| | * it is strictly increasing; |
| | * it is s.t. <math>\alpha(0) = 0</math>. |
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| | '''Definition''': a continuous function <math>\alpha : [0, a) \rightarrow [0, \infty)</math> is said to belong to class <math>\mathcal{K}_{\infty}</math> if: |
| | * it belongs to class <math>\mathcal{K}</math>; |
| | * it is s.t. <math>a = \infty</math>; |
| | * it is s.t. <math>\lim_{r \rightarrow \infty} \alpha(r) = \infty </math>. |
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| | ==See also== |
| | * H. K. Khalil, Nonlinear systems, Prentice-Hall 2001. Sec. 4.4 - Def. 4.2. |
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| | [[Category:Control theory]] |
Revision as of 23:35, 10 January 2013
In control theory, it is often required to check if a nonautonomous system is stable or not. To cope with this it is necessary to use some special comparison functions. Class functions belong to this family:
Definition: a continuous function is said to belong to class if:
- it is strictly increasing;
- it is s.t. .
Definition: a continuous function is said to belong to class if:
See also
- H. K. Khalil, Nonlinear systems, Prentice-Hall 2001. Sec. 4.4 - Def. 4.2.