Class kappa ell function - Alchetron, the free social encyclopedia

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 K functions belong to this family:

Definition: A continuous function β : [ 0 , a ) × [ 0 , ∞ ) → [ 0 , ∞ ) is said to belong to class K L if:

for each fixed s , the function β ( r , s ) belongs to class kappa;

for each fixed r , the function β ( r , s ) is decreasing with respect to s and is s.t. β ( r , s ) → 0 for s → ∞ .

References

Class kappa-ell function Wikipedia

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