Control theory

Class kappa function

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. (Wikipedia).

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Control theory | Class kappa-ell function