Radially unbounded function

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In mathematics, a radially unbounded function is a function for which

Such functions are applied in control theory. Notice that the norm used in the definition can be any norm defined on , and that the behavior of the function along the axes does not necessarily reveal that it is radially unbounded or not; i.e. to be radially unbounded the condition must be verified along any path that results in:

For example the functions

are not radially unbounded since along the line , the condition is not verified even though the second function is globally positive definite.

References

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