View source for Class kappa-ell function

In [[Control theory|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 <math>\mathcal{KL}</math> functions belong to this family:
'''Definition''': A continuous function <math>\beta : [0, a) \times [0, \infty) \rightarrow [0, \infty)</math> is said to belong to class <math>\mathcal{KL}</math> if:
* for each fixed <math>s</math>, the function <math>\beta(r,s)</math> belongs to [[Class kappa function|class kappa]];
* for each fixed <math>r</math>, the function <math>\beta(r,s)</math> is decreasing with respect to <math>s</math> and is s.t. <math>\beta(r,s) \rightarrow 0</math> for <math>s \rightarrow \infty</math>.

==See also==
* [[Class kappa function]]
* H. K. Khalil, Nonlinear systems, Prentice-Hall 2001. Sec. 4.4, Def. 4.3.

[[Category:Control theory]]

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