Sample Time in Adaptation Law

I've got an Adoption Law using a sampling time (T_s) and a number of periods(i) to determinte it's output. All other components of my adaptive controller don't depend expictly on this sample time.

I don't know how to implement this sample and which specific values i should use. If I choose fixed step with a fundamental sample time, then this would affect all other components of the controller, which is not desired? Is it possible to generate a sample time only for this specific Adaption Law-Block? Or is this whole approach wrong?