Exponentially modified Gaussian distribution: Difference between revisions

Revision as of 05:41, 10 December 2013

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 ${\mathcal {K}}$ functions belong to this family:

Definition: A continuous function $\beta :[0,a)\times [0,\infty )\rightarrow [0,\infty )$ is said to belong to class ${\mathcal {KL}}$ if:

for each fixed $s$ , the function $\beta (r,s)$ belongs to class kappa;
for each fixed $r$ , the function $\beta (r,s)$ is decreasing with respect to $s$ and is s.t. $\beta (r,s)\rightarrow 0$ for $s\rightarrow \infty$ .

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+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 function | comparison functions]]. Class <math>\mathcal{K}</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==
+* H. K. Khalil, Nonlinear systems, Prentice-Hall 2001. Sec. 4.4, Def. 4.3.
+[[Category:Control theory]]

Exponentially modified Gaussian distribution: Difference between revisions

Revision as of 05:41, 10 December 2013

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