“Class kappa function”的意思、由来-开放百科全书

词条

Class kappa function

释义

See also

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:

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.

See also