Class-K∞ function

Definition · applies to scalar functions

Graduate (nonlinear control)

Consider a class-$\mathcal{K}$ function $\alpha$ defined on all of $[0, \infty)$. The function $\alpha$ is of class-\(\mathcal{K}_\infty\) if $\alpha(r) \to \infty$ as $r \to \infty$.

Examples

Non-examples

Things that may be mistaken for examples.

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

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