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Class kappa function : ウィキペディア英語版
Class kappa function
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 \mathcal functions belong to this family:
Definition: a continuous function \alpha : [0, a) \rightarrow [0, \infty) is said to belong to class \mathcal if:
* it is strictly increasing;
* it is s.t. \alpha(0) = 0.
Definition: a continuous function \alpha : [0, a) \rightarrow [0, \infty) is said to belong to class \mathcal_ if:
* it belongs to class \mathcal;
* it is s.t. a = \infty;
* it is s.t. \lim_ \alpha(r) = \infty .
==See also==

* H. K. Khalil, Nonlinear systems, Prentice-Hall 2001. Sec. 4.4 - Def. 4.2.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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