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- In control theory, it is often required to check if a 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. . In fact, this is nothing but the definition of the norm except for the triangular inequality. Definition: a continuous function is said to belong to class if:
* it belongs to class ;
* it is s.t. ;
* it is s.t. . A nondecreasing positive definite function satisfying all conditions of class other than being strictly increasing can be upper and lower bounded by class functions as follows: Thus, to proceed with the appropriate analysis, it suffices to bound the function of interest with continuous nonincreasing positive definite functions.In other words, when a function belongs to the it means that the function is radially unbounded. (en)
- 類函數（Class kappa function）也稱為是在控制理論中判斷非自治系統（nonautonomous system）是否穩定時會用到的一類函數，會將其他函數和類函數比較，以確認系統的穩定性。 連續函數若滿足以下條件，則屬於類函數：
* 函數嚴格遞增。
* 函數滿足。 連續函數若滿足以下條件，則屬於類函數：
* 函數屬於類函數。
* 函數的定義域範圍可以到無限大，.
* 函數滿足. 若一非遞減的正定函數滿足所有類（或類）函數的條件，只有嚴格遞增條件不滿足，可以用以下的方式讓此函數的上下界用類（或類）函數來表示： (zh)
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- 類函數（Class kappa function）也稱為是在控制理論中判斷非自治系統（nonautonomous system）是否穩定時會用到的一類函數，會將其他函數和類函數比較，以確認系統的穩定性。 連續函數若滿足以下條件，則屬於類函數：
* 函數嚴格遞增。
* 函數滿足。 連續函數若滿足以下條件，則屬於類函數：
* 函數屬於類函數。
* 函數的定義域範圍可以到無限大，.
* 函數滿足. 若一非遞減的正定函數滿足所有類（或類）函數的條件，只有嚴格遞增條件不滿足，可以用以下的方式讓此函數的上下界用類（或類）函數來表示： (zh)
- In control theory, it is often required to check if a 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. . In fact, this is nothing but the definition of the norm except for the triangular inequality. Definition: a continuous function is said to belong to class if:
* it belongs to class ;
* it is s.t. ;
* it is s.t. . (en)
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- Class kappa function (en)
- K類函數 (zh)
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