Class-K function

Definition · applies to scalar functions

Graduate (nonlinear control)

Consider a function $\alpha : [0, a) \to [0, \infty)$. The function $\alpha$ is of class-$\mathcal{K}$ if

1. $\alpha$ is continuous
2. $\alpha$ is strictly increasing and
3. $\alpha(0) = 0$.

Examples

Examples

• $r \mapsto \arctan r$ on $[0, \infty)$ Graduate

Non-examples

Things that may be mistaken for examples.

• $f(x) = x^2$ on $\reals$ High school

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